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

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

Step-by-step explanation:

A = P ×
`(1+(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 =
`(\ln(64))/(\ln(1.005))`

or

12t = 833.85433

or

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