Question

1a. Your grandmother will be giving you $3,000 per year for the next four years, the first payment beginning at the end of the first year What is the future value of these receivables in year 4 , if the interest rate is 6%?

b. Your grandmother will be giving you $3,000 per year for the next four years, the first payment beginning at the end of the first year What is the future value of these receivables in year 10 , if the interest rate is 6%?

c. You plan to deposit $5,000 each year for the next five years, beginning one year from today, in a bank that pays 8% annual interest. What is the future value of these payments in year 10?

d. You plan to deposit $5,000 each year for the next five years, beginning one year from today, in a bank that pays 8% annual interest. What is the future value of these payments in year 10, if you make one withdrawal of $2,000 in year 8?

Answer #1

This is a Future value of annuity problems, Formula used is FVA = A x [(1+r)^n -1]/r

And FV = PV x (1+r)^n

Prob 1: A = $3000, N = 4, r = 6%

FVA = 3000 x[ (1+.06)^4-1]/.06

FVA = 3000 x [4.374616] = $13,123.85

So future value will be $13,123.85 at the end of 4 years.

Prob 2: PV = FV at end of year 4 = $13,123.85, r = 6%, n = 6 (10
th year – 4^{th} year)

FV = 13123.85x(1+.06)^6

FV in year 10 = $18,616.43

Prob 3: A = 5000, n = 5, r = 8%

FVA = 5000x[(1+.08)^5-1]/.08

FVA = 5000 x 5.8666 = 29333

Next FV in year 10,

FV = 29333x(1+.08)^5 = $43,099.80

Prob 4: Future value in year 5 of Annuity is $29333

FV in Year 8

FV = 29333x(1+.08)^3 = 36951.13

After Withdrawal amount is reduced by $2000, = 34951.13

FV in year 10

FV = 34951.13x(1+.08)^2 = $40,767

So future value in year 10 will be $40,767

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