Piscataway National Bank pays compound interest on savings accounts, but at different rates depending on the amount of the account balance. It pays an annual effective rate of 3% on balances under $10,000, but 4% on balances greater than or equal to $10,000. Suppose that you make a $5,000 deposit. How many years does it take for the account balance to reach $15,000?

It will take 4.2 years

Explanation:

The amount due in the future when a sum of money is invested at a particular interest rate for certain number of years is called Future or compound value.

To calculate the compound value, we use the formula below:

FV = PV * (1+r) ^n

FV - future value, PV - Present value, r - interest rate, n - number of years

In this question,

FV - 15,000, PV - 5000, r - 3%, n-?

Substituting this value we have:

15,000 = 5000 * (1+0.03) ^n

15000 = 5000 * 1.03^n

1.03^n = 15,000/5000

1.03^n = 3

log 1.03^n = Log 3

n = Log 3/log 1.03

n = 4.18735

It will take about 4.2 years for the account to reach $15,000