What payment, made at the end of each year for 9 years, will accumulate to $$ 13, 800$ at $6 %$ compounded monthly?
The required annual payment is $$$
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer

Expert–verified

Hide Steps

Answer

Rounding to the nearest cent gives the final answer: $96.68$

Steps

Step 1 ：Given that the future value (FV) is $13,800, the annual interest rate (r) is 6% or 0.06 in decimal form, the number of compounding periods per year (n) is 12 (since it's compounded monthly), and the number of years (t) is 9.

Step 2 ：The formula for the payment of an annuity when the future value is known is: $P = \frac{F V \times (r / n)}{(1 + r / n)^{n t} - 1}$

Step 3 ：Substitute the given values into the formula: $P = \frac{13800 \times (0.06 / 12)}{(1 + 0.06 / 12)^{12 \times 9} - 1}$

Step 4 ：Solving the equation gives: $P = 96.67934490677582$

Step 5 ：Rounding to the nearest cent gives the final answer: $96.68$

What payment, made at the end of each year for 9 years, will accumulate to $13,800 at 6% compounded monthly?The required annual payment is $(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer

Popular Problems

What payment, made at the end of each year for 9 years, will accumulate to $$ 13, 800$ at $6 %$ compounded monthly?
The required annual payment is $$$
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)