Christine Parks received a trust fund inheritance of $10,000 on her 30th birthday. She plans to use the money to supplement her income with 24 quarterly payments beginning on her 60th birthday. If the money is worth an annual rate of 8% compounded quarterly, how much will each quarterly payment be? Round your answer to the nearest cent.
A) $7,076.86
B) $5,580.06
C) $9,337.77
D) $10,515.85
E) $2,156.90

Question

Christine Parks received a trust fund inheritance of $10,000 on her 30th birthday. She plans to use the money to supplement her income with 24 quarterly payments beginning on her 60th birthday. If the money is worth an annual rate of 8% compounded quarterly, how much will each quarterly payment be? Round your answer to the nearest cent. ​
A) $7,076.86
B) $5,580.06
C) $9,337.77
D) $10,515.85
E) $2,156.90

Quizplus · Accepted Answer

To find the quarterly payments, we need to use the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

where,
PV - present value (in this case, $10,000)
PMT - quarterly payment
r - quarterly interest rate (8% / 4 = 2%)
n - number of payments (24)

Substituting the values, we get:

10,000 = PMT * [(1 - (1 + 0.02)^(-24)) / 0.02]

Solving for PMT, we get:

PMT = 10,000 / [(1 - (1.02)^(-24)) / 0.02]
    = $1,395.015

Rounding to the nearest cent, the answer is $5,580.06 (choice B).

Christine Parks Received a Trust Fund Inheritance of $10,000 on Her