Question

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?

Answer 1

Answer:

You should choose an account with a 7% annual interest rate which is compounded quarterly

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

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  

$t=15\ years\\ P=\ 14,000\\ r=0.07\\n=4$  

substitute in the formula above  

$A=14,000(1+\frac{0.07}{4})^{4*15}$

$A=14,000(1.0175)^{60}$  

$A=\ 39,645.43$  

part 2)

we have  

$t=15\ years\\ P=\ 14,000\\ r=0.068\\n=12$  

substitute in the formula above  

$A=14,000(1+\frac{0.068}{12})^{12*15}$

$A=14,000(1.0057)^{180}$  

$A=\ 38,713.11$