Question

Please answer the following! Thank you!

1.)Jennifer Davis wants to accumulate $16,000 by the end of 12 years. If the annual interest rate is 6.40 percent and interest compounds semiannually, how much will she have to invest today to achieve her goal? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.)

Present value of investment= ?

2)Your brother has asked you for a loan and has promised to pay you $9,100 at the end of three years. If you normally invest to earn 6.90 percent per year, how much will you be willing to lend to your brother if you view this purely as a financial transaction (i.e., you don’t give your brother a special deal)? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.)

Amount To be invested today?

3)Matthew Young is considering an investment that pays 5.40 percent, compounded annually. How much will he have to invest today so that the investment will be worth $27,000 in six years? (Do not round intermediate calculations and round your final answer to the nearest penny.)

Amount to be invested today?

Answer 1

(1) Future Value = $ 16000, Tenure = 12 years or 24 half-years and Rate of Interest = 6.4 % per annum compounded semi-annually

Let the current required investment be $ K

Therefore, K x (1.032)^(24) = $ 16000

K = 16000 / (1.032)^(24) = $ 7512.89

(2) Tenure = 3 years, FV = $ 9100 and Interest Rate = 6.9 %

Amount that can be loaned should be equal to the PV of payout three years from now discounted at the applicable interest rate.

Therefore, Amount that can be loaned = 9100 / (1.069)^(3) = $ 7449.17

(3) Interest Rate on Investment = 5.4 %, Tenure = 6 years and FV = $ 27000

Current Required Investment = 27000 / (1.054)^(6) = $ 19693.37