Homework help Brian wants to save money to purchase a car H

Homework help -

\"Brian wants to save money to purchase a car. He buys an annuity with quarterly payments that earn 2.2% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 3 years if each quarterly payment is $1377. Do not round any intermediate computations, and round your final answer to the nearest cent.\"

Solution

Future value of annuity = Payment * [(1+interest)^{number of period} - 1] / interest

       =$1377 * [(1+2.2%/4)^3years*4 - 1] / (2.2%/4)

   =$1377 * [(1+0.0055)¹² - 1] / 0.0055

=$1377 * [(1.0055)¹² - 1] / 0.0055

=$1377 * [1.068034- 1] / 0.0055

=$1377 *0.068034 / 0.0055

=$17033.24

total value of the annuity in 3 years if each quarterly payment is $1377 is $17033.24 .