The compounding interest formula is :
[tex]A=P(1+\frac{r}{n}^{})^{nt}[/tex]
where A = future amount
P = initial amount
r = interest rate
n = number of compounding
t = time in years.
From the problem, we have :
P = $1200
r = 2.1% or 0.021
n = 52 (compounded weekly)
a. The customized formula will be :
[tex]\begin{gathered} A=1200(1+\frac{0.021}{52})^{52t} \\ A=1200(1.000404)^{52t} \\ A=1200(1.021218)^t \end{gathered}[/tex]
b. The balance after 30 months.
Convert t = 30 months into years
[tex]30\text{mos}\times\frac{1yr}{12\text{mos}}=2.5yrs[/tex]
So t = 2.5 years.
Substitute t = 2.5 :
[tex]\begin{gathered} A=1200(1.021218)^{2.5} \\ A=\$1264.67 \end{gathered}[/tex]
c. Balance after 5 years.
Substitute t = 5 :
[tex]\begin{gathered} A=1200(1.021218)^5 \\ A=\$1332.83 \end{gathered}[/tex]
d. The interest gained after 5 years is the difference between the final amount and the initial amount.
That will be :
[tex]\begin{gathered} I=A-P \\ I=1332.83-1200 \\ I=\$132.83 \end{gathered}[/tex]
