Finance Quiz: Investments and Annuities

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Questions and Answers

If you have $15,000 and need $20,000 for a car, and your investment yields 10% annually, approximately how many years will it take to reach your goal?

3.5 years

2.5 years

3.0 years (correct)

4.0 years

If you want to buy a house for $150,000 and need a 10% down payment plus 5% of the loan amount for closing costs, how much money do you need in total?

$22,500

$16,750

$15,000

$21,750 (correct)

With a $15,000 initial investment and a 7.5% annual return, about how many years will it take to reach the required $21,750 for the down payment and closing costs of a house?

5.5 years

4.0 years

4.5 years

5.1 years (correct)

What is the key characteristic of an ordinary annuity?

Cash flows occur at the end of each period. (C) Signup and view all the answers

Which of the following is an example of an annuity due?

Monthly rent payments (A) Signup and view all the answers

What defines a perpetuity in finance?

An infinite series of equal payments. (D) Signup and view all the answers

How do you calculate the present or future value of an annuity due after computing it as if it were an ordinary annuity?

Multiply by (1+r) (B) Signup and view all the answers

What does the process of discounting primarily determine?

The present value of a future cash flow. (B) Signup and view all the answers

What is the formula to find the present value of a perpetuity where the payment is PMT and the discount rate is r?

PMT / r (C) Signup and view all the answers

If you want to find the present value of $1000 received in 2 years time with an interest rate of 5%, what is the correct calculation?

$1000 / (1.05)^2$ (C) Signup and view all the answers

Assuming the same interest rate, which is true about the relationship between time period and present value?

The longer the time period, the lower the present value. (D) Signup and view all the answers

What tends to happen to the present value of a future sum, as the interest rate increases?

The present value decreases. (C) Signup and view all the answers

If a future value is $2000 and the present value is $1000, and the interest rate was 10%, what is the number of periods(t)?

$ln(2) / ln(1.1)$ (B) Signup and view all the answers

What is the 'discounting factor' used for when finding the present value of a future sum?

It is multiplied by the future sum. (A) Signup and view all the answers

Which of the following Excel functions can be used to compute present value?

PV(rate, nper, pmt, fv) (B) Signup and view all the answers

If you need $10,000 in 2 years and can earn 5% annually, what is the present value you need today?

$10,000 / (1.05)^2$ (D) Signup and view all the answers

If you deposit $1500,$1000 and $500 at the end of each year for the next 3 years, earning a 6% interest rate, what is the present value of these cash flows?

$2,724.90 (D) Signup and view all the answers

Using the same cash flows ($1500, $1000 and $500) and interest rate (6%), what is the future value of these investments at the end of 3 years?

$3,245.40 (D) Signup and view all the answers

What is the combined present value of receiving $1,000 in 7 years and $1,000 in 10 years, assuming a discount rate of 6%?

$1,223.45 (C) Signup and view all the answers

Which of the following best describes the Annual Percentage Rate (APR)?

The annual rate quoted by law. (C) Signup and view all the answers

How do you calculate the per-period interest rate from the APR?

Divide the APR by the number of periods per year. (B) Signup and view all the answers

If you have a credit card with a 1.5% monthly interest rate and a $1,000 balance, approximately how many years will it take to pay off the balance assuming no additional charges?

7.8 years (A) Signup and view all the answers

A loan of $2,000 is taken at a 5% annual interest rate, with annual payments of $734.42. How many years will it take to pay off this loan?

3 years (A) Signup and view all the answers

You borrow $10,000 from your parents to purchase a car, agreeing to pay $207.58 per month for 60 months. What is the monthly interest rate on this loan?

0.75% (A) Signup and view all the answers

Your firm is purchasing a $100,000 warehouse, with the bank requiring a 20% down payment. If the bank offers a 30 year-loan with equal annual payments, what will be the loan amount?

$80,000 (A) Signup and view all the answers

For the warehouse purchase described, if it is a 30-year loan at an 8% annual interest rate, what additional information would be needed to determine the annual loan payment?

No further information is needed (D) Signup and view all the answers

If you know the loan amount, the number of monthly payments and the monthly payment amount, which of these can you calculate?

Monthly interest rate (D) Signup and view all the answers

If you know all other parameters, how does increasing the number of payments affect the annual payment amount while keeping the principle constant?

The annual payment amount decreases (D) Signup and view all the answers

Which function in excel is used to calculate number of periods required to pay off a loan when all other variables are known?

NPER (B) Signup and view all the answers

If the account earns 12% per year, how much will Ellen have saved at age 6, assuming she invested $10,000?

$14,049 (A) Signup and view all the answers

In the Future value of Annuity calculation, what does the variable 'i' represent?

The interest rate per period (B) Signup and view all the answers

In the formula for the future value of an annuity, the variable $n$ usually refers to:

The number of compounding periods. (D) Signup and view all the answers

What is the future value of an annuity used to calculate?

The total value of savings at a specific date. (D) Signup and view all the answers

What does the variable 'P' stand for in the future value of an ordinary annuity formula?

The periodic payment (A) Signup and view all the answers

Using the formula given, if Ellen deposits $20,000 into an account with 7% interest per year, after how many years will she have approximately $6,645 interest earned?

2 years (B) Signup and view all the answers

What is the key difference between calculating the future value of a single sum versus the future value of an annuity?

Annuities consider multiple regular deposits, single sums dont. (B) Signup and view all the answers

If an investment has a negative interest rate, how will this appear in the standard future value of an annuity formula?

The interest rate will be a negative decimal number such as -0.05. (A) Signup and view all the answers

If Ellen makes 3 deposits of $10,000, how many times would the interest earned be compounded in the future value of annuity calculation?

3 times (D) Signup and view all the answers

How many deposits are needed to calculate the 'future value of annuity'?

More than 1 deposit. (A) Signup and view all the answers

What is the primary distinction between the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR)?

APR is the quoted interest rate, while EAR considers the effect of compounding. (C) Signup and view all the answers

Which of the following best describes the term 'm' as used in the formulas for APR and EAR?

The number of compounding periods per year. (B) Signup and view all the answers

If a loan quotes an APR of 10% compounded monthly, what is the value of m in the EAR formula?

12 (B) Signup and view all the answers

Which of the following actions is explicitly discouraged when calculating the period rate?

Dividing the APR by the number of periods per year. (C) Signup and view all the answers

How to calculate the Effective Annual Rate (EAR) with the APR and number of periods per year $m$?

$EAR = (1 + APR/m)^m - 1$ (D) Signup and view all the answers

How to calculate the Annual Percentage Rate (APR) with the Effective Annual Rate (EAR) and number of periods per year $m$?

$APR = m((1 + EAR)^{1/m} - 1)$ (A) Signup and view all the answers

In Excel, which function is used to calculate the effective interest rate when provided with the nominal rate and the number of compounding periods per year?

EFFECT(Nominal_rate, npery) (D) Signup and view all the answers

In Excel, which function is used to calculate the nominal interest rate when provided with the effective interest rate and the number of compounding periods per year?

NOMINAL(Effective_rate, npery) (A) Signup and view all the answers

Given an APR of 8% compounded quarterly, which calculation allows you to find the EAR?

$(1 + 0.08/4)^4 - 1$ (D) Signup and view all the answers

If an investment has an Effective Annual Rate of 10%, and interest is compounded monthly, setup the calculation that finds the Annual Percentage Rate (APR).

$12*((1 + 0.10)^{1/12} - 1)$ (A) Signup and view all the answers

What is the value of 'npery' in the Excel EFFECT and NOMINAL formulas?

The number of compounding periods per year. (B) Signup and view all the answers

If an investment quotes an APR of 12% compounded semi-annually, what is the value of 'm'?

2 (D) Signup and view all the answers

A loan has an EAR of 7.5%. If the interest is compounded quarterly, what setup would find the APR?

$4*((1 + 0.075)^{1/4} - 1)$ (A) Signup and view all the answers

Which rate is typically used for time line visualizations and calculations?

Period Rate (A) Signup and view all the answers

Why should one not divide the effective rate by the number of periods per year?

It won’t give you the correct period rate. (B) Signup and view all the answers

Study Notes

Module 2: Basic Concepts and Application of Time Value of Money

Students should be able to explain compounding and bringing the value of money back to the present
Students should be able to understand annuities
Students should be able to determine future or present value of a sum when there are non-annual compounding periods.
Students should be able to determine the present value of an uneven stream of payments, and understand perpetuities

Lecture Outline

Time value of money
Using timelines to visualize cash flows
Compounding and future value
Discounting and present value
Computing number of periods
Present value or future value of annuities, annuities due, and perpetuities
Computing numbers of periods or interest rates (given variables)
Future and present value of uneven cash flows
Comparing interest rates (APRs versus EARs)
Applications of time value of money

2.1 The concept of time value of money

Money has time value: a dollar today is worth more than a dollar tomorrow.
Reasons for time value:
- Immediate use of money
- Investment opportunities and returns
- Inflation
- Cost avoidance
- Risk of loan non-repayment
Interest rate: exchange rate between earlier money and later money
Need for a return, given value today versus tomorrow
Loss of value from other potential uses must be recognized
Relevant variables in dealing with time value of money:
- Initial amount (principal)
- Time period of the loan
- Interest rate
- Time period to which interest rate applies

2.1 Simple vs. Compound Interest

Simple interest: applied to the principal for a given time period
Compounded Interest: interest earned during the first period is added to the principal, then interest is earned on this new sum during the next period.

2.1 Simple vs. Compound Interest Example

Deposit $500 at 5% annual interest
- Simple Interest: $50 after 2 years; Balance = $550.
- Compound Interest (annually compounding): $51.25 after 2 years; Balance = $551.25

2.2 Using Timelines to Visualize Cash Flows

Timelines identify timing and amount of cash flows along with interest rate.
Tick marks occur at the end of periods (years, months, etc.). Time 0 is today
Timelines are typically expressed in years (also months, days etc).

2.2 Uneven Cash Flow Stream Example

3-year timeline with a 10% interest rate shows a $100 outflow at time 0 followed by $100 $75 and $50 inflows at times 1, 2 and 3 respectively.

2.3 Compounding and Future Value

Future value (FV): Worth of a cash flow in the future
Example: $1,000 invested at 5% for one year:
- FV = $1,050
Example: $1,000 invested at 5% for two years:
- FV = $1,102.50 using the compounding formula

2.3 Compounding and Future Value (Excel Function)

Excel FV function: calculate future value of a sum

2.4 Discounting and Present Value

Present value: What a future cash flow is worth today.
Present value and Future Value are mirror images
Discounting factor: 1 / (1 + r)^t where r is the interest rate and t is the number of periods
Calculating Present Value (using Excel): PV(rate, nper, pmt, fv, type)

2.4 Discounting and Present Value Examples

$10,000 needed in one year at a 7% interest rate = $9,345.79 today
$150,000 needed in 17 years at 8% interest rate = $40,540.34 today
$19,671.51 worth today with a 10-year investment at 7% = $10,000

2.5 Computing Number of Periods

Formula for calculating number of periods t -t =ln(FV / PV)/ln(1 + r)
Example: $15,000 investment at 10% interest to get $20,000 = 3.02 years

2.6 PV or FV of Annuities, Annuities Due and Perpetuities

Annuity: Sequence of equal cash flows at the end of each period (Ordinary Annuity)
Annuity-due: Sequence of equal cash flows at the beginning of each period.
Perpetuity: Infinite series of equal payments

2.6 Annuities and Perpetuities Basic Formulas

Ordinary Annuity Present Value
Ordinary Annuity Future Value
Perpetuity Present Value
Calculating PV/FV of annuity-due (multiple formula)

2.6 PV or FV of Annuities, Annuities Due and Perpetuities Examples

Calculate the present value of $632 monthly payments over 48 months at 1% per month
Calculate the future value of $10,000 yearly payments over 30 years at 10% per year
Calculate present value of an annual graduation party that costs $30,000

2.7 Using Excel's Functions to compute one variable given Relevant Variables

Excel functions for time value of money used
- FV, PV, NPER, RATE, PMT

2.7 Using Excel's Functions to compute one variable given Relevant Variables: Examples

Calculate monthly payment for a $20,000 loan at 8% annual interest over 4 years.
Calculate time to pay off a $1000 credit card debt with $20 monthly payments at 1.5% interest rate.
Calculate interest rate for a $10,000 loan with $207.58 monthly payments over 60 months

2.8 Future and Present Value of Uneven Cash Flows

Calculate Present Value of Uneven cashflow
- NPV(rate, CF₁, CF₂, ..., CFN) + CF₀

2.8 Future and Present Value of Uneven Cash Flows: Examples

Present value of $1500, $1000 and $500 in three years when bank interest is 6%
Future value of $1500, $1000 and $500 in three years when the bank interest is 6%

2.9 Comparing Interest Rates: APRs vs EARs

Effective Annual Rate (EAR): Actual rate after compounding.
Annual Percentage Rate (APR): Annual rate quoted by law
APR = Period rate * number of periods per year (used in calculations)
Example: Calculate APR if 12% effective interest rate with monthly compounding

2.9 Comparing Interest Rates: APRs vs EARs, Examples

Comparing two savings accounts with different compounding periods:
Calculate EAR of 21.7% APR with daily compounding.

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Description

Test your knowledge on financial concepts related to investments, annuities, and present value calculations. This quiz covers scenarios involving investment growth, down payments for houses, and key characteristics of various financial products. It's a great way to sharpen your finance skills!