Question

(a) Suppose you have a 1-year old son and you want to provide $75,000 in 20 years toward his college education. You currently have $5,000 to invest. What interest rate must you earn to have the $75,000 when you need it?

(b) An investment will provide you with $800 at the end of each year for the next 20 years. If you deposit those payments into an account earning 8%, calculate the future value in 20 years.

(c) You want to receive $1,000 at the end of every month for the next 5 years. Calculate the amount you need to deposit today if you can earn 0.5% per month

(d) Suppose you have $200,000 today. You expect that you can earn 0.5% per month. How much could you receive at the end of every month for 5 years?

Answer 1

Solution:

a. Given that Future Value, FV = 75,000, Present Value, PV = $5,000, Number of years, n = 20 and interest rate, i = ?

We use the following equation to find the interest rate,

FV = PV (1 + i)^n

75,000 = 5,000 (1 + i)^20

(1 + i)^20 = 15

i = (15)^(1/20) - 1

i = 0.15 or 15%

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b. Given that Annuity, A = $800, Interest rate, i = 8% and Number of years, n = 20

The future value of the annuity, FVA is given by the equation

FVA = A (FVIFA @ i, n)

FVA = $800 (FVIFA @ 8%, 20)

FVA = 800 (45.71696)

FVA = $36,609.57

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c. Given that Annuity, A = $1,000 Number of periods, n = 5*12 = 60, Interest rate, i = 0.5% and Present value of annuity, PVA = ?

The present value of annuity, PVA is calculated using the equation

PVA = A (PVIFA @ i, n)

PVA = $1,000 (PVIFA @ 0.5%, 60)

PVA = $1,000

PVA = $1,000 (51.72556)

PVA = $51,725.56

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d. Given that Present Value, PV = $200,000, Interest rate, i = 0.5% and Number of period, n = 5*12 = 60 and Annuity, A = ?

The annuity is calculated using the equation

PV = A (PVIFA @ i, n)

$200,000 = A (PVIFA @ 0.5%, 60)

$200,000 = A

$200,000 = A (51.72556)

A = $3,866.56