Question

Tracey sets aside $35,000 in a bank account today with the aim of becoming more liquid. The account pays 5 percent compounded monthly. Due to the fact that deposit insurance covers the account for only $100,000, compute how many months it will take to reach that amount.

Answer 1

Amount deposited = $35,000
Targeted balance = $100,000
Annual interest rate = 5.00%
Monthly interest rate = 0.4167%

Let number of months required to achieve the targeted balance be n

Amount deposited * (1 + Monthly interest rate)^Period = Targeted balance
$35,000 * 1.004167^n = $100,000
1.004167^n = 2.85714
n * ln(1.004167) = ln(2.85714)
n = 252.46

Number of months = 252.46

So, it will take 252.46 or 252 months to reach targeted balance of $100,000