Diego decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account?

Answer: it will take 17.5 years to double his money in the account.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P (1+r/n) ^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $500

A = 500 * 2 = $1000

r = 4% = 4/100 = 0.04

n = 4 because it was compounded 3 times in a year.

Therefore,.

1000 = 500 (1 + 0.04/4) ^4 * t

1000/500 = (1 + 0.01) ^4t

2 = (1.01) ^4t

Taking log of both sides, it becomes

Log2 = 4tlog 1.01

0.301 = 4t * 0.0043 = 0.0172t

t = 0.301/0.0172

t = 17.5 years

Answer: it will take 17.5 years to double his money in the account.