Question

The amount of money in a bank account that is compounded yearly can be represented by the function A(y) = P(1 + r)y, where P is the amount initially deposited, r is the annual interest rate expressed as a decimal, and y is the number of years that have passed since the initial deposit. $2,700 was deposited 14 years ago into a bank account that is compounded yearly, and no additional deposits or withdrawals have been made. If the amount of money now in the bank account is $7,930.42, what is the annual interest rate?

A) about 5%
B) about 6%
C) about 7%
D) about 8%

Answer 1

D

Explanation:

7930.42 = 2700(1+r)¹²

(1+r)¹⁴ = 2.9371925926

14×ln(1+r) = ln2.9371925926

ln(1+r) = 0.076961016

1+r = e^0.076961016

1+r = 1.0799999729

r = 0.0799999729 × 100

= 8%

Answer 2

The correct option is D. The interest is about 8%.

Explanation:

The amount of money in a bank account that is compounded yearly can be represented by the function

`A(y)=P(1+r)^y`

Where P is the amount initially deposited, r is the annual interest rate expressed as a decimal, and y is the number of years that have passed since the initial deposit.

The initial amount is $2700, numbers of years is 14 and the amount after 14 years is $7930.42.

`7930.42=2700(1+r)^(14)`

`2.937=(1+r)^(14)`

Taking log both sides.

`log2.937=log(1+r)^(14)`
`(loga^b=bloga)`

`0.4679=14log(1+r)`

`0.033422=log(1+r)`

`10^(0.033422)=10^(log(1+r))`

`1.079999=1+r`
`(10^(loga)=a)`

`0.079999=r`

`r\approx 0.08`

Therefore the correct option is D. The interest is about 8%.