Question

After 6 years, what is the total amount of a compound interest investment of $35,000 at 4% interest, compounded quarterly?

Answer 1

$9441

Explanation:

The interest will be compounded quarterly every year, it means in each year the interest will be calculated 4 times.

In 6 years in total
`6 *4` = 24 times the interest will be calculated.

The yearly interest rate is 4%. Hence, the quaterly interest rate will be
`(4)/(4)<strong>` = 1%.

Hence, after calculating 24 times, the amount will be turned to
`35000 * ((101)/(100) )^(24)` = 44440.7127≅ 44441.

Hence, the total compound interest is $(44441 - 35000) = $9441

Answer 2

The amount of investment after 6 years is $ 44439.5

Explanation:

Given as :

The principal amount = p = $ 35,000

The rate of interest = r = 4 % compounded quarterly

The time period of loan amount = t = 6 years

Let The Amount after 6 years = $ A

So, From compounded method

Amount = Principal ×
`(1+(\textrm rate)/(4* 100))^(4* \textrm time)`

Or, A = P ×
`(1+(\textrm r)/(4* 100))^(4* \textrm t)`

Or, A = $ 35000 ×
`(1+(\textrm 4)/(4* 100))^(4* \textrm 6)`

or, A = $ 35000 ×
`(1.01)^(24)`

Or, A = $ 35000 × 1.2697

∴ A = $ 44439.5

So, Amount after 6 years = $ A = $ 44439.5

Hence The amount of investment after 6 years is $ 44439.5 Answer