Suppose that you have a series of payments: $100 in year 1, $150 in year 2 and $200 in year 3. If annual interest rate is 10%, what is the equivalent annuity for this series?
A)$150.00
B)$146.82
C)$142.33
D)$140.11
E)$135.68

Question

Quizplus · Accepted Answer

The equivalent annuity can be calculated using the present value of the given series of payments and then converting it into an annuity over the given period at the given interest rate. First, calculate the present value (PV) of each payment:- PV of $100 in year 1 = $100 / (1 + 0.10)^1 = $90.91- PV of $150 in year 2 = $150 / (1 + 0.10)^2 = $123.97- PV of $200 in year 3 = $200 / (1 + 0.10)^3 = $150.26Total PV = $90.91 + $123.97 + $150.26 = $365.14Now, find the equivalent annuity using the formula for the present value of an annuity: PV = A * [(1 - (1 + r)^-n) / r], where A is the annuity payment, r is the interest rate, and n is the number of periods. Rearrange to solve for A:A = PV / [(1 - (1 + r)^-n) / r] = $365.14 / [(1 - (1 + 0.10)^-3) / 0.10] = $365.14 / 2.4869 = $146.82

Suppose That You Have a Series of Payments: $100 in Year