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

Option C) 16.01%

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(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+(r)/(4))^(4*7)`

`3=(1+(r)/(4))^(28)`

Apply log both sides

elevated both sides to 1/28

`\sqrt[28]{3}=(1+(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\%`