Question

10. Na'il Diggs deposited $6,500 into a savings account paying 6% annual interest,

compounded monthly. How much compound interest did he earn in 3 months?

Answer 1

$97.99

Explanation:

3 months is "fraction" of a year

How much?

3/12 = 1/4th of a year

So, the interest earned in 3 months, is annual interest divided by 4.

We can use compound interest formula shown below to solve this easily:

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

Where

A is the future amount

P is the present amount (principal)

r is the rate of interest annual

n is the number of compounding in a year

t is the time in years

So, let's find the given information:

P = 6500

r = 6% = 6/100 = 0.06

n = 12 [compounded monthly, so 12 times compounding]

t = 1/4 = 0.25 [3 months = 0.25 of a year]

Now, substituting, we find the value of 6500 after 3 months:

`A=P(1+(r)/(n))^(nt)\\A=6500(1+(0.06)/(12))^(12*0.25)\\A=6500(1.005)^(3)\\A=6597.99`

So 6500 became 6597.99 in 3 months. The excess amount is the interest earned.

Interest Earned = 6597.99 - 6500 = $97.99