Question

Suppose you deposit $125 into an account at the end of every month. If the account earns 6% interest, compounded monthly, how long (in years) will it take for the value of the account to reach $8000? Round your answer to two decimal places.

Answer 1

Answer:

t = 69.4879 years ≈ 69 years 5 months and 27 days

Explanation:

A = P × $(1+\frac{r}{n})^{nt}$

Here,

A = total amount  = $8,000

P = principal or amount of money deposited = $125

r = annual interest rate  = 6%

n = number of times compounded per year  = monthly i.e 12

t = time in years

thus,

$8,000 = $125 × $(1.005)^{12t}$

or

$(1.005)^{12t}$ = 64

taking natural log both the sides, we get

$\ln((1.005)^{12t})$ = ln(64)

or

12t × ln(1.005) = ln(64)

or

12t = $\frac{\ln(64)}{\ln(1.005)}$

or

12t = 833.85433

or

t = 69.4879 years ≈ 69 years 5 months and 27 days