Answer :
Answer:
The time needed is 4 years.
Step-by-step explanation:
The formula to compute the amount in case of compound interest is:
[tex]A=P\ [1+\frac{r\%}{n}]^{nt}[/tex]
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:
[tex]A=P\ [1+\frac{r\%}{n}]^{nt}[/tex]
[tex]23177.80=19000\ [1+\frac{0.05}{4}]^{4\times t}\\\\\frac{23177.90}{19000}=(1.0125)^{4t}\\\\1.21989=(1.0125)^{4t}\\\\\log (1.21989)=4t\cdot \log(1.0125)\\\\4t=\frac{\log (1.21989)}{\log(1.0125)}\\\\4t=16\\\\t=4[/tex]
Thus, the time needed is 4 years.