Answer:
It will take 17.2 years to reach account balance of $16826.03
Step-by-step explanation:
Given
Principal amount P = $ 8534
rate of interest r = 4% = 4/100 = 0.04
No of times interest is compounded, n = 12
Final amount A = $ 16826.03
To find: time in years, t = ?
We know that final amount of compound interest A is given by formula:
A = P [tex](1 + \frac{r}{n} )^{nt}[/tex]
Substituting known values,
16826.03 = 8534 * [tex](1 + \frac{0.04}{12} )^{12t}[/tex]
[tex](1 + \frac{0.04}{12} )^{12t}[/tex] = 1.972
[tex](1.0033)^{12t}[/tex] = 1.972
take log on both sides,
ln [tex](1.0033)^{12t}[/tex] = ln (1.972)
12t * ln (1.0033) = ln (1.972) (since ln [tex]x^{n}[/tex] = n * ln x)
12t = 206.112
t = 17.2 years
