Question

You currently have $5,100. first united bank will pay annual interest rate of 8.6, while second national bank will pay you an annual interest rate of 9.7. how many fewer years must you wait for your account value to grow to $11,200 at second National bank?

Answer 1

First United Bank:

Amount Deposited = $5,100
Desired Sum = $11,200
Interest Rate = 8.60%

Let it will take n years to reach the desired balance

Amount Deposited * (1 + Interest Rate)^Period = Desired Sum
$5,100 * 1.086^n = $11,200
1.086^n = 2.196078
n * ln(1.086) = ln(2.196078)
n = 9.54 years

It will take 9.54 years to reach the desired balance if amount is deposited in first united bank.

Second National Bank:

Amount Deposited = $5,100
Desired Sum = $11,200
Interest Rate = 9.70%

Let it will take n years to reach the desired balance

Amount Deposited * (1 + Interest Rate)^Period = Desired Sum
$5,100 * 1.097^n = $11,200
1.097^n = 2.196078
n * ln(1.097) = ln(2.196078)
n = 8.50 years

It will take 8.50 years to reach the desired balance if amount is deposited in second national bank.

So, you have to wait 1.04 years less if you deposit in second national bank