Question

suppose you deposit $2000 in a savings account that pays interest at an annual rate of 5% if no money is added or withdrawn from the account how many years will it take for the account to contain $2500 and how many years will it take for the account to contain $3000

Answer 1

• $2500: 4.57 years
• $3000: 8.31 years

Explanation:

The time required for an account earning compound interest to achieve a particular balance is given by the formula ...

t = log(A/P)/(n·log(1 +r/n))

where principal P is compounded n times per year at annual rate r. A is the account balance after that time. For this problem, n=1.

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a.

Here, we have ...

P = $2000, A = $2500, r = 0.05, n = 1

The number of years is ...

t = log(2500/2000)/log(1.05) ≈ 4.57 . . . years

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b.

For A = $3000, this becomes ...

t = log(3000/2000)/log(1.05) ≈ 8.31 . . . years