Jay's bank account listed a balance of $3,667.50. He originally opened the account with a $3,070 deposit 2 1/4 years ago. If there were no deposits or withdrawals, what was the simple interest rate (to the nearest hundredth of a percent)?

1 Answer
Mar 23, 2018

See below.

Explanation:

If you just want the percentage of the total interest after 2.25 years.

3667.50/3070xx100%=119.46%

We started with 100%, this was our $3070.

The amount extra is:

19.56%

Below is a more realistic answer, since interest is calculated at specified periods. Often monthly, quarterly or yearly.

The amount of interest after 2.25 years is:

We can use the formula for compound interest, with 1 compound per year.

FV=PV(1+r/n)^(nt)

Where:

FV="future value"

PV="principal value"

r="interest rate as a decimal"

n="compounding period"

t="time in years"

Our future value is what we have now. $3667.50

Our principal value is what we started with $3070.00

Compounding period is 1 i.e. once a year.

Time is 2.25 years.

We need to find bbr, the interest rate.

Putting in our known values:

3667.50=3070(1+r/1)^(2.25)

Divide by 3070:

3667.50/3070=(1+r)^(2.25)

Taking logarithms of both sides:

ln(3667.50/3070)=2.25ln(1+r)

Divide by 2.25:

(ln(3667.50/3070))/2.25=ln(1+r)

Using the laws of logarithms:

y=ln(b)=>e^y=b

Using this idea. Raise bbe to the power of both sides:

e^((ln(3667.50/3070))/2.25)=e^(ln(1+r))

(3667.50/3070)^(1/2.25)=1+r

r=(3667.50/3070)^(1/2.25)-1

r~~0.082244085

This is in decimal form, so multiplying by 100.

8.22% percent per year.