Respuesta :
Investments worth $4487.19 in total at the end of 3 years.
Solution:
Principal, P = 2000
Rate, R = 4% compounded quarterly
Rate, R = 3.75% compounded annually
Year, n = 3
Formula for compound interest when compounded quarterly:
[tex]Amount=P(1+\frac{\frac{R}{4} }{100})^{4n}[/tex]
Substitute P = 2000, R = 4% and n = 3
[tex]Amount=2000\times(1+\frac{\frac{4}{4}}{100})^{4\times3}[/tex]
[tex]=2000\times(1+\frac{1}{100})^{12}[/tex]
[tex]=2000\times(\frac{100+1}{100})^{12}[/tex]
[tex]=2000\times(\frac{101}{100})^{12}[/tex]
= 2253.65
Amount when compound interest calculated quarterly is 2253.65.
Formula for compound interest when compounded annually:
[tex]Amount=P(1+\frac{R}{100})^{n}[/tex]
Substitute P = 2000, R = 3.75% and n = 3
[tex]Amount=2000\times(1+\frac{3.75}{100})^{3}[/tex]
[tex]=2000\times(\frac{100+3.75}{100})^{3}[/tex]
[tex]=2000\times(\frac{103.75}{100})^{3}[/tex]
= 2233.54
Amount when compound interest calculated annually is 2233.54.
Total amount = 2253.65 + 2233.54
= 4487.19
Hence, investments worth $4487.19 in total at the end of 3 years.
