Questions and Answers
What annual interest rate is required to double an investment in 7 years with annual compounding?
If an investment of 8,000 amounts to 8,820 at a 10% interest rate compounded half-yearly, how long does it take for the investment to mature?
What is the total number of conversion periods if 200,000 amounts to 231,525 in 1½ years with interest compounded half-yearly?
If a principal of `78,030 amounts to what sum when invested at 4% per annum compounded semi-annually for one year?
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In the calculation for doubling an investment, which equation is used?
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What is the interest rate per conversion period if the annual rate is 10% compounded semi-annually?
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What is the formula used to determine the amount after n periods with compounded interest?
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What too long period must an investment earn interest to amount to 231,525 if starting from 200,000 at 5% compounded semi-annually?
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What is the initial deposit amount if the total amount reaches `1,01,500 with interest applied at a rate of 2% for 6 years?
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If a sum of 46,875 lent out at simple interest results in a total amount of 50,000 after 1 year and 8 months, what is the interest rate per annum?
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What sum of money will produce `28,600 as interest in 3 years and 3 months at an interest rate of 2.5% per annum?
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In how many years will an investment of 85,000 amount to 1,57,675 at an interest rate of 4.5% per annum?
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What is the total interest earned from a principal of `70,000 after 6 years at a rate of 2% per annum?
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Given that a principal of 46,875 earns an interest of 3,125 over one year, what is the effective rate of interest?
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If 1,00,000 is deposited and the total amount after 3 years is 1,20,000 at simple interest, what is the rate of interest per annum?
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What will be the total amount after 5 years if `50,000 is invested at an interest rate of 3% per annum?
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What is the formula used to calculate the present value of a cash flow stream with growth?
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If the discount rate is 7% and the growth rate is 5%, what is the discount factor for the cash flow of 50?
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What does calculating the rate of return enable an investor to do?
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Why is net present value (NPV) used in evaluating capital investments?
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Which attribute is important for successful investors when making investment decisions?
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What does the net present value method specifically take into account?
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What would be a consequence of continually making losing investments?
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If an investment generates cash flows at different times, what concept helps in comparing these cash flows?
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What constitutes the principal in the context of investment?
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Which formula is used to calculate compound interest?
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How is the effective rate of interest computed?
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In the context of annuities, what characterizes an annuity due?
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What is the formula to calculate the future value of a single cash flow?
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What does the variable 'n' represent in the context of compound interest?
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Which of the following statements is true regarding annuity payments?
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If the annual interest rate is denoted by 'i', how is the interest 'I' calculated?
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What is the formula used to calculate the final value of an investment at simple interest?
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If Rahul received 85,925 after investing 70,000 at a simple interest rate of 6.5% per annum for a certain period, what was the calculated period?
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How much interest would Sachin earn on a deposit of ` 1,00,000 at a 6% simple interest rate over 2 years?
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What rate of interest corresponds to an amount owed of 1050 on a borrowed amount of 1000 after 6 months?
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What is the initial deposit made by Kapil if he received ` 1,01,500 after 7.5 years at a simple interest rate of 6%?
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Using the formula A = P(1 + it), if P = ` 50,000 and i = 5.5% for 2 years, what is the final amount, A?
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What is the amount of interest generated if an amount of ` 70,000 is invested for 3.5 years at a simple interest rate of 6.5%?
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What is the total final value of Sachin's bank deposit after earning interest?
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Study Notes
Investment and Interest Calculation
- The final value of investment can be calculated using the formula: ( A = P(1 + it) ).
- For an investment of ₹50,000 at a simple interest rate of 5.5% over 2 years, the final amount is ₹55,500.
Simple Interest Calculation
- Simple interest formula: ( I = P \times it ), where ( P ) is principal, ( i ) is rate, and ( t ) is time.
- Example: Sachin deposits ₹100,000 at a 6% interest rate for 2 years, earning ₹12,000 interest, leading to a total of ₹112,000.
Rate of Interest Determination
- Given an amount of ₹1,050 after 6 months from an initial loan of ₹1,000, the interest rate can be calculated as 10%.
Period Calculation from Amount
- When Rahul invested ₹70,000 at a 6.5% interest rate and received ₹85,925, the investment period calculated is 3.5 years.
Initial Deposit Calculation
- Kapil received ₹101,500 after 7.5 years at a 6% interest rate; his initial deposit was calculated to be ₹70,000.
Interest Rate Computation Over Time
- For ₹46,875 that grew to ₹50,000 over 1 year and 8 months, the interest rate found was 4%.
Principal Calculation from Interest Earned
- A sum needed to yield ₹28,600 interest over 3 years and 3 months at 2.5% p.a. was calculated to be ₹352,000.
Time Calculation for Investment
- The time required for ₹85,000 to double to ₹157,675 at 4.5% p.a. interest can be derived via ( A_n = P(1 + i)^n ).
Compounding Annual Interest
- An investment doubling in 7 years at a compounded annual rate can be calculated, leading to a required interest rate of 10.41%.
Semiannual Compounding Example
- ₹8,000 growing to ₹8,820 at a 10% per annum interest rate compounded semiannually takes 1 year.
Compound Interest Calculation
- Formula for compound interest: ( A_n = P(1 + i)^n ), where ( n ) is the total number of compounding periods.
Effective Rate of Interest
- The effective interest rate formula: ( E = (1 + i)^n - 1 ).
Annuities
- An annuity is a series of periodic payments; it can either be regular (payments at the end of periods) or due (payments at the beginning).
- To compute future value of a cash flow, use the formula ( F = C.F.(1 + i)^n ), where ( C.F. ) is the cash flow.
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Description
Test your knowledge on calculating final investment values using the formula A = P(1 + it). This quiz will cover concepts related to principal amounts, interest rates, and time periods. It's perfect for students studying finance or accounting.
