Question

Scott currently has an account balance of $2,147.39. He opened the account five years ago with a deposit of $1,852.10. If the interest compounds monthly, what is the interest rate on the account? (3 points) Select one: a. 0.2% b. 10.5% c. 3.0% d. 5.9%

Answer 1

1852.10(1+x%)=2,147.39

1+x%=1.15

x%=0.15

so t it B i think

Answer 2

Option c - 3%

Explanation:

Given : Scott currently has an account balance of $2,147.39. He opened the account five years ago with a deposit of $1,852.10.

To find : If the interest compounds monthly, what is the interest rate on the account?

Solution :

The compound interest formula is

`A=P(1+(r)/(n))^(nt)`

Where, A is the amount A=$2,147.39

P is the principal P=$1,852.10

t is the time t= 5 years

n is the number of time compounded n=12

r is the interest rate

Substitute all the values in the formula,

`2147.39=1852.10(1+(r)/(12))^(12* 5)`

`(2147.39)/(1852.10)=(1+(r)/(12))^(60)`

`1.159=(1+(r)/(12))^(60)`

Taking ln both side,

`\ln (1.159)=60\ln (1+(r)/(12))`

`0.1479=60\ln (1+(r)/(12))`

`(0.1479)/(60)=\ln (1+(r)/(12))`

`0.00245=\ln (1+(r)/(12))`

Taking exponential both side,

`e^(0.00245)=1+(r)/(12)`

`1.00245=1+(r)/(12)`

`1.00245-1=(r)/(12)`

`0.00245* 12=r`

`0.0294=r`

Into percentage,
`r=0.0294* 100=2.94\%`

Approximately, The interest rate on the account is 3%.

Therefore, Option c is correct.