Question

Joan invests $800 at 12.5% per anum compound intrest compounded daily.What is the amount of intrest at the end of first year?

Answer 1

Answer:

$106.50

Step-by-step explanation:

We should use the compound interest formula:

$A=P\left(1+\frac{r}{n}\right)^{nt}$

Where P is the amount of money invested thus $800

r is the annual rate in decimal form thus 0.125 (since 12.5%/100 yields to that)

n is the number of periods the interest is compound during the year, thus 365 since the interest is compounded daily and there are 365 days in a year.

t is the number of years which is 1 year

And A is the future value after a year.

Therefore, the formula becomes:

$A=800\left(1+\frac{0.125}{365}\right)^{365(1)}$

We put that in the calculator and we get:

A = $906.50

The interest is the difference between this future value and the money invested:

I = $906.50 - $800  = $106.50

And that is the amount of interest at the end of first year.

Answer 2

A=P(1+i)^n
P=800
i=0.125/12 (12.5/100 to get from percentage to normal and /12 to convert from year to months)
n=12
A=800(1+0.125/12)^12
=905.93
Therefore , Interest = 905.93-800
=105.93