Question

Jose is making quarterly contributions of of $210 to his savings account which pays interest at the APR of 5.9%, compounded quarterly. Right after Jose makes his 53rd contribution, the bank changes the APR to 8.1% and Jose makes 47 more $210 contributions. What is Jose's balance right after his last contribution?

Please show work written out.

Answer 1

When i = 5.9% = 5.9% / 4 = 1.475% per quarter

When i = 8.1% = 8.1% / 4 = 2.025% per quarter

Account's worth at 53rd deposit = 210 * (F/A, 1.475%,53)

= 210 * ((1 + 0.01475)^53-1)/0.01475

= 210 * ((1.01475)^53-1)/0.01475

= 210 * 79.515401

= 16698.23

Account's worth at 100th deposit = 16698.23 * (F/P, 2.025%,47) + 210 * (F/A, 2.025%,47)

= 16698.23 * (1 + 0.02025)^47 + 210 * ((1 + 0.02025)^47-1)/0.02025

= 16698.23 * (1.02025)^47 + 210 * ((1.02025)^47 - 1)/0.02025

= 16698.23 * 2.565727 + 210 * 77.319828

= 59080.26