Question

The local bank pays 4% interest on savings deposits. In a nearby town, the bank pays 1% per quarter. A man who has $2945 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 more money would he obtain if the out-of-town bank was chosen?

Answer 1

Solution:-

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.

a)Amount of money to be received after 3 years if nearby town bank is chosen.

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

                =$2945*(1+0.04)³ = $2945*1.12486=$3,312.72

b) Amount of money to be received after 3 years if out of town bank is chosen.

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%

Substituting the value in above equation

Amount to be received=$2945*(1+0.01)¹² =$2945*1.126825 =$3,318.50

Hence additional amount received

= Amount received from out of town bank -Amount received from nearby town bank

=$3,318.50-$3,312.72

=$5.78

Hence he would receive additional $5.78 .

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