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?

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

step-by-step explanation: