If you make quarterly payments of $455.00 into an ordinary annuity earning an annual interest rate of 3.97% compounded quarterly, how much will you have in the account after 7 years?
Answer (2)
After making quarterly payments of $455 into an ordinary annuity with an annual interest rate of 3.97% compounded quarterly for 7 years, the future value of the account will be approximately $14,643.99.
;
Calculate the quarterly interest rate: i = 4 0.0397 = 0.009925 .
Calculate the total number of payment periods: n = 7 × 4 = 28 .
Use the future value of an ordinary annuity formula: F V = P × i ( 1 + i ) n − 1 .
Substitute the given values into the formula and calculate the future value: F V = 14643.99 .
Explanation
Understanding the Problem We are given the quarterly payment amount, the annual interest rate compounded quarterly, and the number of years. We need to find the future value of the ordinary annuity.
Calculating the Quarterly Interest Rate First, we need to calculate the quarterly interest rate. The annual interest rate is 3.97%, so the quarterly interest rate is: i = 4 0.0397 = 0.009925
Calculating the Number of Payment Periods Next, we need to calculate the total number of payment periods. The annuity is for 7 years, and payments are made quarterly, so the total number of payment periods is: n = 7 × 4 = 28
Stating the Future Value Formula Now, we can use the future value of an ordinary annuity formula to calculate the future value of the annuity. The formula is: F V = P × i ( 1 + i ) n − 1 where:
F V is the future value of the annuity
P is the payment amount per period
i is the interest rate per period
n is the number of periods
Calculating the Future Value We are given that the quarterly payment amount is P = $455.00 . Substituting the values we calculated earlier, we get: F V = 455 × 0.009925 ( 1 + 0.009925 ) 28 − 1 F V = 455 × 0.009925 ( 1.009925 ) 28 − 1 F V = 455 × 0.009925 1.319426 − 1 F V = 455 × 0.009925 0.319426 F V = 455 × 32.1846 F V = 14643.99
Final Answer Therefore, the future value of the annuity after 7 years is approximately $14643.99 .
Examples
Annuities are commonly used in retirement planning. For example, if you want to save for retirement, you can make regular contributions to an annuity account. The annuity will grow over time due to the interest earned, and when you retire, you can receive regular payments from the annuity. Understanding how annuities work and how to calculate their future value can help you make informed decisions about your retirement savings.
