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

Answer:

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

Step-by-step 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%.

Answer 2

Answer:

D

Step-by-step 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%