MATH SOLVE

3 months ago

Q:
# Say you have $14,000 to invest into an investment account. You can either invest your money into an account with a 7% annual interest rate which is compounded quarterly, or an account with a 6.8% annual interest rate which is compounded monthly, which should you choose for a 15-year investment?

Accepted Solution

A:

Answer:You should choose an account with a 7% annual interest rate which is compounded quarterlyStep-by-step explanation:we know that The compound interest formula is equal to [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where A is the Final Investment Value P is the Principal amount of money to be invested r is the rate of interest in decimal
t is Number of Time Periods n is the number of times interest is compounded per year
part 1) we have [tex]t=15\ years\\ P=\$14,000\\ r=0.07\\n=4[/tex] substitute in the formula above [tex]A=14,000(1+\frac{0.07}{4})^{4*15}[/tex] [tex]A=14,000(1.0175)^{60}[/tex]
[tex]A=\$39,645.43[/tex]
part 2) we have [tex]t=15\ years\\ P=\$14,000\\ r=0.068\\n=12[/tex] substitute in the formula above [tex]A=14,000(1+\frac{0.068}{12})^{12*15}[/tex] [tex]A=14,000(1.0057)^{180}[/tex]
[tex]A=\$38,713.11[/tex]