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

Answer:

option (c) $18,032

Step-by-step 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 × $\frac{(1+r)^n-1}{r}$

here, r is the interest rate

n is the duration

thus,

Future value = $1 × $\frac{(1+0.0002192)^{7300}-1}{0.0002192}$

or

Future value = $18033.56 ≈ $18,032

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