Question

How long will it take for $600 to grow to $47,500 at an interest rate of 8% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Answer 1

It will take about 55.19 years.

To find this problem, we have to solve the following equation.

Answer 2

The formula for compound interest is given by:

$A=P(1+\frac{r}{n}) ^{nt}$

where,

A=amount,

P=principal

r=rate of interest

t=time(years)

n=number of times the interest is compounded annually.

Now we are given,

A=amount = 47,500

P=principal= 600

r=rate of interest= 8% or 0.08

n= 4 ( quarterly)

t=time(years)= is to be found

Plugging these in the formula,

$47500=600(1+\frac{0.08}{4}) ^{4t}$

$47500=600(1.02) ^{4t}$

$79.167=(1.02) ^{4t}$

On solving, we get

t=55.19 years

Answer: It will take 55.19 years for $600 to amount to $47,500.