Question

How much time will be needed for $19,000 to grow to $23,177.90 if deposited at

5% compounded quarterly?

Answer 1

The time needed is 4 years.

Explanation:

The formula to compute the amount in case of compound interest is:

`A=P\ [1+(r\%)/(n)]^(nt)`

A = amount

P = principal

r = interest rate

n = number of periods

t = years

The information provided is:

A = $23,177.90

P = $19,000

r = 5%

n = 4

Compute the value of t as follows:

`A=P\ [1+(r\%)/(n)]^(nt)`

`23177.80=19000\ [1+(0.05)/(4)]^(4* t)\\\\(23177.90)/(19000)=(1.0125)^(4t)\\\\1.21989=(1.0125)^(4t)\\\\\log (1.21989)=4t\cdot \log(1.0125)\\\\4t=(\log (1.21989))/(\log(1.0125))\\\\4t=16\\\\t=4`

Thus, the time needed is 4 years.