Name/Time PV &FV; Practice Problems In Class Homework Chapter 6 1 Page What do y
ID: 2550322 • Letter: N
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Name/Time PV &FV; Practice Problems In Class Homework Chapter 6 1 Page What do you have to invest today at 12% interest in order to have S 10,000 in two years? Assume interest compounds annually 2. What if the interest compounds quarterly? 3. What if the interest compounds monthly? An investor decides to deposit S 10,000 a year at an interest rate of 10% compounded annually. Find the future value of this annuity immediately after the fourth deposit An individual realizes that they will need $20,736 per year for the next four years. The first payment is needed one year from today. If they can find an investment returning 20% compounded annually, how much would they need to invest today to receive the four payments? 5. What is the value of a single deposit of S 15,000 that earns 10% interest compounded annually in four years? 7. What interest rate must be carned in order to produce a future amount of $14,963.20 in six years from a deposit of $8,0002Explanation / Answer
1) In the given question, we need to determine present value of $10,000 discounted at given interest rate of 12%.
Formula: Present Value = Future Value / (1+r)n
Where, r is interest rate per period and n is number of periods.
Amount to be deposited today = $10,000 / (1+0.12)2 = $7,971.94
2) If compounding of interest happens more than once a year, the effective interest rate will be higher than the quoted interest rate. So, we first need to calculate the effective interest rate.
Formula: Effective Interest Rate = [(1) + (r/n)]n – 1
Effective interest rate with quarterly compounding = [(1) + (0.12/4)]4 – 1 = 0.125509
Amount to be deposited today = $10,000 / (1+0.125509)2 = $7,894.09
3) Effective interest rate with monthly compounding = [(1) + (0.12/12)]12 – 1 = 0.126825
Amount to be deposited today = $10,000 / (1+0.126825)2 = $7,875.66
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