A principal of $2100 is invested at 7.5% interest, compounded annually. How many years will it take to accumulate $5000 or more in the account?

Question

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Answer 1

7.5% annual interest means that after 1 year, you have 1.075 times as much as you had at the beginning of the year.  If the starting amount is A₀ and this process goes on for n years, the final amount will be

 

A(n) = A₀ x 1.075ⁿ

 

A₀ = $2100

 

A(n) = ($2100) (1.075ⁿ)

 

To find how long it takes to reach $5000, set A(n) = $5000 and solve for n.

 

$5000 = ($2100) (1.075ⁿ)

 

2.381 ≅ 1.075ⁿ

 

log2.381 = n log1.075 

 

n = log2.381 / log1.075 = 11.995 years ≅ 12 years