Question

First City Bank pays 8 percent simple interest on its savings account balances, whereas Second City Bank pays 8 percent interest compounded annually. If you made a $55,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 8 years?

Answer 1

Answer:

you would earn $11,601.16 more money from your Second City Bank account at the end of 8 years.

Explanation:

This can be determined using the following 3 steps:

Step 1: Calculation of Balance in First City Bank account after 8 years

This can be calculated as follows:

Simple interest for 8 years = Deposit * First City Bank simple interest rate * Number of years = $55,000 * 8% * 8 = $35,200

Balance in the First City Bank account after 8 years = Deposit + Simple interest for 8 years = $55,000 + $35,200 = $90,200

Step 2: Calculation of Balance in Second City Bank account after 8 years

This can be calculated using the following formula:

Future value = Balance in Second City Bank account after 8 years = Principal * (1 + r)^n .......... (1)

Where:

Principal = Deposit = $55,000

r = interest rate = 8%, or 0.08

n = number of years

Substituting the values into equation (1), we have:

Balance in Second City Bank account after 8 years = $55,000 * (1 + 0.08)^8 = $101,801.16

Step 3: Calculation of excess of interest earned from Second City Bank account over interest earned from First City Bank account

This can be calculated as follows:

Excess interest earned = Balance in Second City Bank account after 8 years - Balance in the First City Bank account after 8 years = $101,801.16 - $90,200 = 11,601.16

Therefore, you would earn $11,601.16 more money from your Second City Bank account at the end of 8 years.