Question

I need help with question 2 abcd I started but not sure if I am doing it right

Answer 1

The compounding interest formula is :

`A=P(1+(r)/(n)^{})^(nt)`

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 :

`\begin{gathered} A=1200(1+(0.021)/(52))^(52t) \\ A=1200(1.000404)^(52t) \\ A=1200(1.021218)^t \end{gathered}`

b. The balance after 30 months.

Convert t = 30 months into years

`30\text{mos}*\frac{1yr}{12\text{mos}}=2.5yrs`

So t = 2.5 years.

Substitute t = 2.5 :

`\begin{gathered} A=1200(1.021218)^(2.5) \\ A=\$1264.67 \end{gathered}`

c. Balance after 5 years.

Substitute t = 5 :

`\begin{gathered} A=1200(1.021218)^5 \\ A=\$1332.83 \end{gathered}`

d. The interest gained after 5 years is the difference between the final amount and the initial amount.

That will be :

`\begin{gathered} I=A-P \\ I=1332.83-1200 \\ I=\$132.83 \end{gathered}`