Question

What annual rate of interest is required to triple an investment in 7 years if it were compounded quarterly?

A) 10.409%

B) 16.993%

C) 16.01%

D) 8.497%

Answer 1

Answer:

Option C) 16.01%

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

in this problem we have  

$t=7\ years\\P=\ x\\A=\ 3x\\n=4$  

substitute in the formula above  

$3x=x(1+\frac{r}{4})^{4*7}$  

$3=(1+\frac{r}{4})^{28}$  

Apply log both sides

elevated both sides to 1/28

$\sqrt[28]{3}=(1+\frac{r}{4})$

Multiply by 4 both sides to remove fraction

$4\sqrt[28]{3}=4+r$

subtract 4 both sides

$r=4\sqrt[28]{3}-4$

$r=0.1601$

convert to percentage

$r=0.1601*100=16.01\%$