Question

A woman dies, leaving her only surviving daughter an estate of $50,000.  The money is invested at j (4) = 8%.  How many quarterly payments of $1500 will the daughter receive?  What would be the amount of any final payment, were it to be paid 3 months after the last full $1500 installment?

Answer 1

Payout Annuity Formula

P0 = d*[{1 - (1+r/k)^(-N*k)}]/(r/k)

P0 is the balance in the account at the beginning = $50000

d is the regular withdrawal = $1500

r is the annual interest rate = 8%

k is the number of compounding periods in one year = 4

N is the number of years we plan to take withdrawals = ?

50000 = 1500*[{1 - (1+0.08/4)^(-x*4)}]/(0.08/4)

0.66667 = 1 - (1.02)^(-4x)

(1.02)^(-4x) = 1 - 0.66667

1.02^(-4x) = 0.33333

take log of both sides

log_e(1.02)^(-4x) = log_e(0.3333)

-4x*log_e(1.02) = -1.09873 {Logm^n = n log m}

-4x*0.019805 = -1.09873

x = 1.09873/(4*0.019805)

= 13.8695 Years

in quarter = 13 Years + 0.8695*12

= 13 Years + 10.434 months

= 13 years + 9 months + 1.43 months

total quarter will be = 13*4 + 9/3 + 1.43months

= 55 quarters & 1.43 months.

daughter will receive 55 Quaterly payments.

and the amount of fnal payment will be = $ 706.73, Yes it is to be paid 3months after the last full $1500 installment.

Amortization schedule of the payment -

Please check with your answer and let me know.