Respuesta :
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;
[tex]\begin{gathered} I\text{ = }\frac{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{ = }\frac{35,000\times4.25\times8}{100}\text{ = \$11,900} \end{gathered}[/tex]Next is to calculate the future value
Mathematically, that is the interest added to the amount invested
We have this as;
[tex]FV\text{ = 11,900 + 35,000 = \$46,900}[/tex]b) Compound interest
To calculate the compound interest value, we are going to use the compound interest formula
Mathematically, we have this as;
[tex]\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\times8} \\ A=35,000(1.0425)^8 \\ A\text{ = 48,829} \end{gathered}[/tex]This is the future value for the compound interest
The interest will be;
[tex]\begin{gathered} \text{Interest = Amount - Principal} \\ \text{Interest = 48,829-35000 = \$13,829} \end{gathered}[/tex]