Question

You believe in the power of compounding and decide to save $1 per day by avoiding the purchase of a soda. You deposit the $1 at the end of each day in a bank account that pays 8% interest compounded daily. You are going to take a trip in 20 years with the money you have accumulated. How much money will you have in 20 years, assuming 365 days per year?

a. $7,500
b. $12,438
c. $18,032
d. $22,456

Answer 1

option (c) $18,032

Explanation:

Data provided in the question;

Amount deposited at the end of each day = $1

Interest paid = 8% compounded daily = 0.08

Daily interest rate =
`\frac{\textup{0.08}}{\textup{365}}` = 0.000219

Duration = 20 years = 20 × 365 days = 7300 days

Now,

the Future value is given as:

Future value = Part payment ×
`((1+r)^n-1)/(r)`

here, r is the interest rate

n is the duration

thus,

Future value = $1 ×
`((1+0.0002192)^(7300)-1)/(0.0002192)`

or

Future value = $18033.56 ≈ $18,032

Hence, the correct answer is option (c) $18,032