Question

Benjamin invests $400 in a savings account that earns 5% interest each year.

Which expression gives the balance in the account after 3 years?
Choose 1 answer:
A
400+ 0.05 -0.05 -0.05
®
400 - 0.05 - 0.05 -0.05
©
400+ (1 + 0.05)(1+0.05)(1 + 0.05)
©
400(1+0.05)(1 + 0.05)(1+0.05)

Answer 1

correct expression is 400 (1+0.05) (1+0.05) (1+0.05)

Explanation:

Given:

Amount invested initially = $400

Interest per year = 5% = 5/100 = 0.05

To find : Balance after 3 years

We know that the formula for final amount A with initial mount P and rate of interest for t years is given by

A = P (1+rt)

For calculating balance in year 1, P = $400, r = 0.05, t = 1

A = 400 (1+(0.05 x 1))

= 400 (1+0.05)

For calculating balance in year 2, P = 400 (1+0.05), r = 0.05, t=1

A = 400 (1+0.05) (1+(0.05 x 1))

= 400 (1+0.05) (1+0.05)

For calculating balance in year 3, P = 400 (1+0.05), r = 0.05, t=1

A = 400 (1+0.05) (1+0.05) (1+(0.05 x 1))

= 400 (1+0.05) (1+0.05) (1+0.05)

Hence the expression that gives balance account in 3 years is 400 (1+0.05) (1+0.05) (1+0.05)