Question

A savings account is started with an initial deposit of $700. The account earns 1.5% interest compounded

annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $1,200. Show your work.
Answer:

Answer 1

(a) A = 700×1.015^t

(b) 36.2 years

Explanation:

(a) Each year, the account value is multiplied by (1 + 1.5%) = 1.015. Repeated multiplication is signified using an exponent. In t years, when the account has been multiplied by 1.015 t times, the account value will be ...

A = $700×1.015^t

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(b) You want to find t when A=$1200. Logarithms are involved.

1200 = 700×1.015^t . . . . use 1200 for A

1200/700 = 1.015^t . . . . . divide by 700

log(12/7) = t×log(1.015) . . . . . take logarithms

log(12/7)/log(1.015) = t ≈ 36.2 . . . . divide by the coefficient of t

It will take about 36.2 years for the account balance to reach $1200.