Simple Interest and Loans Overview

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the correct definition of principal in a loan context?

The amount of interest paid to the lender

The amount of money that is being borrowed (correct)

The total amount paid for a loan

The total repayment amount including interest

What is the formula for calculating the maturity value in simple interest?

F=P+I (correct)

F=P(1-rt)

F=P(1+rt) (correct)

F=P-I

Which equation is used to calculate the interest rate in a simple interest scenario?

r=t/I

r=I/Pt (correct)

r=P/It

r=IPt

What does the term 'loan proceeds' refer to in terms of discount interest?

The actual amount received by the borrower Signup and view all the answers

Which equation correctly represents the interest rate in simple interest calculations?

r=I/Pt Signup and view all the answers

What is the correct formula for determining time in simple interest?

t=I/Pr Signup and view all the answers

What is the total amount paid for a loan known as?

Maturity value Signup and view all the answers

Which statement accurately describes simple interest?

It is computed only from the original amount borrowed Signup and view all the answers

Which two equations provide the formula for maturity value in simple interest?

F=P+I Signup and view all the answers

What is the term for the actual amount received by the borrower in discount interest?

Loan Proceeds Signup and view all the answers

Which formula correctly represents how to find the time involved in a simple interest calculation?

t=I/Pr Signup and view all the answers

Which statement regarding simple interest is accurate?

Statement II only. Signup and view all the answers

If a borrower wants to understand the effective borrowing cost, which amount should they examine?

Maturity value Signup and view all the answers

How is ordinary interest generally defined?

None of the above. Signup and view all the answers

What is the periodic rate if an amount is compounded quarterly at an 8% annual rate?

0.04 Signup and view all the answers

Which of these options correctly identifies the payments made at equal intervals?

Annuity Signup and view all the answers

What is the compound interest on an initial amount of P506.17 after 2 years?

P807.71 Signup and view all the answers

How many days approximate time elapsed if Lyka's loan is from September 18, 2022, to November 7, 2022, at 3% simple interest?

49 Signup and view all the answers

What is the ordinary simple interest for Lyka's loan using the approximate time calculated?

P61.25 Signup and view all the answers

If Cris borrows P1,000 at 6% interest compounded monthly, how much total does he need to repay after a year?

P1,061.68 Signup and view all the answers

What interest rate compounded annually is required for an investment to grow from 18 million pesos to 25 million pesos in 8 years?

4.19% Signup and view all the answers

What is the total interest that Cadex will pay on a loan of P40,000.00 at an interest rate of 1% over 9 months?

P300 Signup and view all the answers

What annual interest rate is required for an investment of P1,000 to earn P150 in 36 months?

5% Signup and view all the answers

How many years will it take for P1,000 to grow to P4,000 at an annual interest rate of 1%?

300 years Signup and view all the answers

If Caden borrows P2,000 for 6 months at a simple interest rate of 10% annually, what is the interest he must pay back?

P200 Signup and view all the answers

What is the exact interest amount owed on a Php 40,000.00 loan at a 10% interest rate for 200 days?

P2,191.78 Signup and view all the answers

What would be the loan proceeds for a loan of P100,000 at a 0.9% discount interest rate to be repaid in 4 years?

P96,400 Signup and view all the answers

How much should EZ Photo Company deposit now to afford copying machines costing P15,000, given an interest rate of 8% compounded semiannually over 2.5 years?

P12,328.91 Signup and view all the answers

What total amount must Cris repay after borrowing Php 40,000 at a monthly compounded interest rate of 1% for 2 years?

P40,807.71 Signup and view all the answers

Study Notes

Simple Interest

Simple interest is calculated only on the principal amount
Formula for simple interest: I = Prt
- I = simple interest
- P = Principal
- r = interest rate (annual rate expressed as a decimal)
- t = time (in years)
The maturity value (F) is the total amount owed at the end of the loan term.
- Formula for maturity value: F = P + I or F = P(1 + rt)
The Discount is the amount deducted from the principal of a loan before the borrower receives the money.
- Formula for discount: D = Prt
The loan proceeds are the actual amount received by the borrower after the discount is deducted.
- Formula for loan proceeds: P’ = P – D or P’ = P(1 – rt)
Ordinary interest uses a 360-day year.
Exact interest uses a 365-day year.
To determine if the actual number of days in a month must be considered, exact interest is to be used, and if not, ordinary interest is to be used.

Compound Interest

Compound interest is calculated on the principal amount and also on the accumulated interest from previous periods
Formula for compound interest: A = P(1 + r/n)^nt
- A = accumulated amount
- P = Principal
- r = interest rate (annual rate expressed as a decimal)
- n = number of compounding periods per year
- t = time (in years)
The periodic rate is the interest rate applied per compounding period.
- Formula for periodic rate: i = r / n
The compounding period is the time between each interest calculation.
- The number of compounding periods per year (n) will determine the compounding period.
Annuity is a series of equal payments made at equal intervals.
Approximate time refers to the number of days assuming 30 days in a month
Actual time refers to the exact number of days in a month

Formulas

Interest rate (r): r = I/Pt
Time (t): t = I/Pr
Maturity value (F): F = P+I, or F = P(1+rt)
Discount (D): D = Prt
Loan Proceeds (P’): P’ = P – D, or P’ = P(1 – rt)

Problem Solving

Borrowed money from the bank is considered as a loan.
When solving for simple interest, it will always use the given interest rate.
When solving for compound interest, it will always use the given principal amount and time.
When solving for an annuity, it will always use the given payment amount and the number of payments.
When solving for actual time, it will always count the number of days in a month.
When solving for approximate time, it will always assume 30 days in a month.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore the fundamentals of simple interest, including key formulas for calculating interest, maturity value, discounts, and loan proceeds. Understand the difference between ordinary and exact interest and learn when to apply each method. This quiz is ideal for students studying basic finance principles.