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

Answer:

4 years Option A: $8,700

6 years Option B: $9034

Answer 2

Solution:

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

$S.I=\frac{P\times R\times T}{100}$

$S.I_{1}=\frac{7500 *4*4}{100}=1200\\\\ S.I_{2}=\frac{7500 *4*6}{100}=1800$

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.

$A=P*(1+\frac{R}{100})^t$

$A_{4}=7500*(1+\frac{3.15}{100})^4\\\\ A_{4}=7500*(\frac{103.15}{100})^4\\\\ A_{4}=7500*(1.0315)^4\\\\ A_{4}=7500*1.1320\\\\ A_{4}=8490.60$

$A_{6}=7500*(1+\frac{3.15}{100})^6\\\\ A_{6}=7500*(\frac{103.15}{100})^6\\\\ A_{6}=7500*(1.0315)^6\\\\ A_{6}=7500*1.2045\\\\ A_{6}=9033.9286$

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

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