You won a contest and your prize will be paid in two installments. You will rece

Question

You won a contest and your prize will be paid in two installments. You will receive the first payment, of $5,000, today and the second payment, of $8,000 at the end of the 6th year. You will deposit this money, at the time each is received (now and at the end of year 6), into a savings account that will earn 10% interest. If you want to withdraw some amount “C” at the end of each year for the first six years and then “C+$500” each year for the next six years (i.e. years 7-12), find the value of C so that the total amount withdrawn equals the total amount deposited.

do not use excel

Explanation / Answer

You won a contest and your prize will be paid in two installments.

You will receive the first payment, of $5,000, today and the second payment, of $8,000 at the end of the 6th year.

You will deposit this money, at the time each is received (now and at the end of year 6), into a savings account that will earn 10% interest.

Future Value of the above deposits at the end of 6th year

FV (at 6th year) = $5,000 (1 + .10) ^ 6 + $8,000 = 8,858 + 8,000 = 16, 858

If you want to withdraw some amount “C” at the end of each year for the first six years and then “C+$500” each year for the next six years (i.e. years 7-12), find the value of C so that the total amount withdrawn equals the total amount deposited.

(Considering Future Value at 6th year the present year to calculate C)

Future worth at 6th year = [C + $500 (A/G, 10%, 6)] (P/A, 10%, 6)

$16, 858 = [C + $500 (2.2236)] (4.3553)

$16, 858 = [C + 1112] (4.3553)

$16, 858 = [4.3553C + 4843]

$16, 858 – 4,843 = 4.3553C

$12, 015 = 4.3553C

C = $12, 015 ÷ 4.3553

C = 2,759

Verification

[2759 + $500 (2.2236)] (4.3553)

[3871] (4.3553) = 16,859

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