Question

if $35,000 is invested at 4:25% for 8 years find the interest and the future value for each station simple interest and compound interest.

Answer 1

a) Simple interest

Interest = $11,900

Future value = $46,900

b) Compound interest

Interest = $13,829

Future value = $48,829

Here, we want to get the simple interest and the compound interest

a) Simple Interest

To get the simple interest, we use the simple interest formula

Mathematically, we have this as follows;

`\begin{gathered} I\text{ = }(PRT)/(100) \\ \\ I\text{ = interest} \\ R\text{ = rate = 4.25\%} \\ T\text{ = time = 8 years} \\ P\text{ = principal = \$35,000} \\ \\ \text{Substituting these values} \\ I\text{ = }(35,000*4.25*8)/(100)\text{ = \$11,900} \end{gathered}`

Next is to calculate the future value

Mathematically, that is the interest added to the amount invested

We have this as;

`FV\text{ = 11,900 + 35,000 = \$46,900}`

b) Compound interest

To calculate the compound interest value, we are going to use the compound interest formula

Mathematically, we have this as;

`\begin{gathered} A=P(1+r)^(nt) \\ A\text{ is the future value/ amount} \\ P\text{ is the invested amount = \$35,000} \\ r\text{ is the interest rate = 4.25\% = 4.25/100 = 0.0425} \\ n\text{ is the number of compounding times per year = 1} \\ t\text{ is the number of years = 8} \\ \\ A=35,000(1+0.0425)^(1*8) \\ A=35,000(1.0425)^8 \\ A\text{ = 48,829} \end{gathered}`

This is the future value for the compound interest

The interest will be;

`\begin{gathered} \text{Interest = Amount - Principal} \\ \text{Interest = 48,829-35000 = \$13,829} \end{gathered}`