Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the 30th year. Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?
A) $500
B) $490
C) $540
D) $570

Question

Quizplus · Accepted Answer

To calculate the present value of an annuity, we need to use the formula:

PV = A * (1 - (1 / (1 + r)^n)) / r

Where PV is the present value, A is the annuity payment, r is the interest rate, and n is the number of payments.

In this case, Charlie wants to receive an annuity of $1,000 a year for 20 years after he retires in 30 years. So, the number of payments n is 20, and the first payment comes at the end of the 30th year, so we need to discount it back 30 years to calculate the present value.

r = 10% or 0.1
n = 20
A = $1,000

PV = $1,000 * (1 - (1 / (1 + 0.1)^20)) / 0.1 * (1 + 0.1)^-30
PV = $540.17

Therefore, Charlie needs to invest $540.17 today to have an annuity of $1,000 for 20 years after he retires in 30 years. Rounded to the nearest $10, the answer is $540.

Charlie Stone Wants to Retire in 30 Years, and He