Answer:
Step-by-step explanation:
For an initial amount P invested at compound interest for a number of years, n compounded at a rate r% periodically with period, k:
Amount[tex]=P(1+\frac{r}{k})^{nk}[/tex]
For the given problem:
P=$5,000; r=4%-=0.04, n=3 years
Annually
k=1
Amount
[tex]=5000(1+\frac{0.04}{1})^{3*1}\\=5000(1.04)^3\\=\$5624.32[/tex]
Semi-Annually
k=2
Amount
[tex]=5000(1+\frac{0.04}{2})^{3*2}\\=5000(1.02)^{6}\\=\$5630.81[/tex]
Quarterly
k=4
Amount
[tex]=5000(1+\frac{0.04}{4})^{3*4}\\=5000(1.01)^{12}\\=\$5634.13[/tex]
Monthly
k=12
Amount
[tex]=5000(1+\frac{0.04}{12})^{3*12}\\=5000(1+\frac{0.04}{12})^{36}\\=\$5636.36[/tex]
