Question

The local bank pays 5% interest on savings deposits. In a nearby town, the bank pays 1.25% per quarter. A man who has $4000 to deposit wonders whether the higher interest paid in the nearby town justifies driving there. If all money is left in the account for 3 years, how much interest would he obtain from the out-of-town bank?

Answer 1

1.25% per quarter, it means 1.25%*4 = 5% yearly

Even though it is seen that they are paying same interest rate, the effective interest rate of out-of-town bank will be higher due to quarterly compounding.

1. Amount of money to be received after 3 years he obtain from the local bank

Amount= Saving*(1+interest rate)^years

=$4000*(1+0.05)³ = $4000*1.157625=$4630.5

2. Amount of money to be received after 3 years he obtain from the out-of-town bank

Amount to be received= Initial saving*(1+perodic interest rate)^periods

Since the amount is quarterly compounded the total number of periods = 3*4 = 12

Periodic interest rate= 1.25%

Put the values in the formula, we get

Amount to be received= $4000*(1+0.0125)¹² =$4000*1.16075452 =$4643.01807

Hence he will received additional

= Amount received from out of town bank -Amount received from nearby town bank(or local bank)

= 4643.01807 - 4630.5

=$12.518

Hence he would receive additional $12.52