6) An inheritance will be $50,000. The interest rate for the time value of money

Question

6) An inheritance will be $50,000. The interest rate for the time value of money is 8%. How much is the inheritance worth now, if it will be received in 20 years?

7)A man borrowed $1250 from a bank. He agreed to repay the sum at the end of 3 years, together with the interest at 6% per year. How much will he owe the bank at the end of 3 years?

8) A sum of $5,000 is invested for five years with varying annual interest rates of 9%, 8%, 12%, 6%, and 15%, respectively. The future amount after 5 years is most nearly equal to ?

9) What is the present value of a series of $2500 payments at the end of each year for 10 years at 5% compounded annually?

10) Pete borrows $15,000 to purchase a used car. He must repay the loan in 48 equal end-of-period monthly payments. Interest is calculated at 1 1/6 % per month. The amount of the monthly payment for this loan is most nearly.

11) Jerry bought a house for $250,000 and made a $50,000 down payment. He obtained a 30-year loan for the remaining amount. Payments were made monthly. The nominal annual interest rate was 5%. What was his monthly loan payment?

Explanation / Answer

6) PV = FV/(1+i)n

PV = 50000/(1+0.08)20 = $10727.41

7) FV = PV * (1 + i)n

FV = 1250 * (1 + 0.06)3 = $1488.77

8) FV at the end of first year = 5000 * (1 + 0.09) = $5450

    FV at the end of first year = 5450 * (1 + 0.08) = $5886

    FV at the end of first year = 5886 * (1 + 0.12) = $6592.32

    FV at the end of first year = 6592.32 * (1 + 0.06) = $6987.86

    FV at the end of first year = 6987.86 * (1 + 0.15) = $8036.04

9)

PV interest rate factor for uniform series payment = [(1+i)n - 1]/[i*(1+i)n]

                                                                       = [(1+0.05)10 - 1]/[0.05 * (1+0.05)10] = 7.72

PMT = payment per period

PV = PMT * PV interest rate factor = 2500 * 7.72 = $19304.34

10) i = 7/6% = 0.012

PV interest rate factor for uniform series payment = [(1+i)n - 1]/[i*(1+i)n]

                                                             = [(1+0.012)48 - 1]/[0.012 * (1+0.012)48] = 36.59

PMT = payment per period

PMT = PV / PV interest rate factor = 15000/36.59 = $409.90

11) i = 5%

PV interest rate factor for uniform series payment = [(1+i)n - 1]/[i*(1+i)n]

                                                           = [(1+0.05/12)360 - 1]/[0.05 * (1+0.05/12)360] = 186.3

PMT = payment per period

PMT = PV / PV interest rate factor = (250000-50000)/186.3 = $1073.64

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