Question

7. You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar.Regular withdrawal:$2100Interest rate:2%FrequencyweeklyTime:19 yearsAccount balance: $

Answer 1

The formula required is expressed as

Po = [d(1 - (1 + r/k)^- nk]/(r/k)

Where

Po is the balance in the account initially

d is the regular amount being withdrawn

r is the interest rate

k is the number of compounding periods in one year

n is the number of years

From the information given,

d = 2100

r = 2/100 = 0.02

n = 19

k = 52(assuming there are 52 weeks in a year)

Thus,

Po = [2100(1 - (1 + 0.02/52)^- 19 * 52]/(0.02/52)

Po = [2100(1 - (1.00038461538)^- 988]/0.00038461538

Po = 2100(0.3161)/0.00038461538

Po = 1725906

The amount that the account needs is $1725906