Solution:
Principal =P= $ 7,500
Option A→(Simple interest)
Rate of interest= R=4%
Time([tex]T_{1}[/tex])=4 years
Time([tex]T_{2}[/tex])=6 years
Amount= Principal + Interest(Simple or compound interest)
Formula for Simple interest
[tex]S.I=\frac{P\times R\times T}{100}[/tex]
[tex]S.I_{1}=\frac{7500 *4*4}{100}=1200\\\\ S.I_{2}=\frac{7500 *4*6}{100}=1800[/tex]
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.
[tex]A=P*(1+\frac{R}{100})^t[/tex]
[tex]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[/tex]
[tex]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[/tex]
Total amount after 4 years when interest is compounded annually=$ 8491 (approx)
Total amount after 6 years when interest is compounded annually=$ 9034(approx)
