Question

Linda deposits $1,800 into an account that pays 7.5% interest, compounded annually. Anna deposits $4,000 into an account that pays 5% interest, compounded annually. If no additional deposits are made to either account, what is the balance of each at the end of 10 years? (to the nearest dollar)

A) Linda's account: $3,710
Anna's account: $6,516
B) Linda's account: $2,315
Anna's account: $5,860
C) Linda's account: $2,647
Anna's account: $6,102
D) Linda's account: $3,150
Anna's account: $4,200

Answer 1

A) Linda's account: $3,710 ; Anna's account: $6,516

Explanation:

Compound interest equations are of the form

`A=p(1+r)^t`, where p is the amount of principal, r is the interest rate as a decimal number and t is the number of years.

For Linda's account,

`A=1800(1+0.075)^(10)\\\\=1800(1.075)^(10)\\\\=3709.86`

To the nearest dollar this rounds to $3710.

For Anna's account,

`A=4000(1+0.05)^(10)\\\\=4000(1.05)^(10)\\\\=6515.58`

To the nearest dollar this rounds to $6516.

Answer 2

A is your answer because Since the interest is compounded annually, the balances grow exponentially.

,A = P( 1 + r/n)nt
Linda = 1800(1 + 0.075)10 = ≈ $3,710
Anna = 4000( 1 + 0.05)10 = ≈ $6,516