Question

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

Answer 1

Answer:

$9441

Step-by-step 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 $6 \times4$ = 24 times the interest will be calculated.

The yearly interest rate is 4%. Hence, the quaterly interest rate will be $\frac{4}{4}$ = 1%.

Hence, after calculating 24 times, the amount will be turned to $35000 \times (\frac{101}{100} )^{24}$ = 44440.7127≅  44441.

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

Answer 2

Answer:

The amount of investment after 6 years is $ 44439.5

Step-by-step 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 × $(1+\dfrac{\textrm rate}{4\times 100})^{4\times \textrm time}$

Or, A = P × $(1+\dfrac{\textrm r}{4\times 100})^{4\times \textrm t}$

Or, A = $ 35000 × $(1+\dfrac{\textrm 4}{4\times 100})^{4\times \textrm 6}$

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