Question

Gavin has $7,500 to invest. He is considering two investment options. Option A pays 4% simple interest. Option B pays 3.15% interest compounded annually. Drag dollar amounts to the table to show the value of each investment option after 4 years and after 6 years rounded to the nearest dollar.

Answer 1

4 years Option A: $8,700

6 years Option B: $9034

Answer 2

Principal =P= $ 7,500

Option A→(Simple interest)

Rate of interest= R=4%

Time(
`T_(1)`)=4 years

Time(
`T_(2)`)=6 years

Amount= Principal + Interest(Simple or compound interest)

Formula for Simple interest

`S.I=(P* R* T)/(100)`

`S.I_(1)=(7500 *4*4)/(100)=1200\\\\ S.I_(2)=(7500 *4*6)/(100)=1800`

Total amount after 4 years when interest is simple= 7500 +1200= $ 8700

Total amount after 6 years when interest is simple= 7500 +1800= $ 9300

Option B

Formula for amount(A) when interest is 3.15% compounded annually.

`A=P*(1+(R)/(100))^t`

`A_(4)=7500*(1+(3.15)/(100))^4\\\\ A_(4)=7500*((103.15)/(100))^4\\\\ A_(4)=7500*(1.0315)^4\\\\ A_(4)=7500*1.1320\\\\ A_(4)=8490.60`

`A_(6)=7500*(1+(3.15)/(100))^6\\\\ A_(6)=7500*((103.15)/(100))^6\\\\ A_(6)=7500*(1.0315)^6\\\\ A_(6)=7500*1.2045\\\\ A_(6)=9033.9286`

Total amount after 4 years when interest is compounded annually=$ 8491 (approx)

Total amount after 6 years when interest is compounded annually=$ 9034(approx)