What amount will an ordinary annuity be worth in 25 years if quarterly payments of $1,750 are made and the interest rate is 14% compounded quarterly for the first 15 years and 10% compounded quarterly for the final 10 years?
A) $384,999
B) $461,859
C) $1,509,570
D) $1,062,754
E) $1,041,360

Question

Quizplus · Accepted Answer

To solve this, we break the problem into two parts because the interest rate changes after 15 years. First, calculate the future value of the annuity for the first 15 years with a 14% annual interest rate compounded quarterly. Then, take that amount and calculate what it will grow to in the next 10 years with a 10% annual interest rate compounded quarterly, while continuing the quarterly payments of $1,750.For the first 15 years:- Quarterly interest rate = 14% / 4 = 3.5%- Number of quarters = 15 * 4 = 60Using the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$Where:- $FV$ is the future value of the annuity.- $P$ is the payment amount per period ($1,750).- $r$ is the interest rate per period (3.5% or 0.035 as a decimal).- $n$ is the total number of payments (60).$FV_{15years} = 1750 \times \frac{(1 + 0.035)^{60} - 1}{0.035}$For the next 10 years:- Quarterly interest rate = 10% / 4 = 2.5%- Number of quarters = 10 * 4 = 40We first calculate the future value of the amount accumulated in the first 15 years without additional payments, and then calculate the future value of the annuity for the next 10 years with the $1,750 quarterly payments.$FV_{total} = FV_{15years} \times (1 + 0.025)^{40} + 1750 \times \frac{(1 + 0.025)^{40} - 1}{0.025}$This calculation is complex and typically requires a financial calculator or spreadsheet software to compute accurately. The correct answer, after performing these calculations, is approximately $1,041,360, which corresponds to option E.

What Amount Will an Ordinary Annuity Be Worth in 25