Question

Bill Baxter has $25,000 to invest for a year. He can lend it to his sister, who has agreed to pay 9% simple interest for the year. Or, he can invest it in a retirement plan expected to pay 8% compounded quarterly for a year. How much additional interest would the simple interest loan to his sister generate?

Answer 1

For a principal P and a simple interest rate r for the year, the simple interest loan after a year is given by the formula:

`I_s=P\cdot r`

For P = $25000 and r = 9% = 0.09, we have:

`\begin{gathered} I_S=0.09\cdot25000 \\ I_S=\text{ \$2250} \end{gathered}`

For an interest rate r' compounded quarterly, after a year the total amount would be:

`A=P\cdot(1+(r^(\prime))/(4)^{})^4`

For P = $25000 and r = 8% = 0.08, we have:

`\begin{gathered} A=25000\cdot(1+(0.08)/(4))^4 \\ A=\text{ \$27060.80} \end{gathered}`

Then, in this case the interest is given by:

`I_C=A-P=27060.80-25000=\text{ \$2060.80}`

Therefore, the simple interest loan would generate 2250 - 2060.80 = $189.20 additional interest in comparisson to the retirement plan