question 12 (5 points)\nlisten\nthe present value of the money in your savings account is $420, and youre…

question 12 (5 points)\nlisten\nthe present value of the money in your savings account is $420, and youre receiving 3% annual interest compounded monthly. what is the future value in two months?\na) $432.60\nb) $424.11\nc) $426\nd) $422.10

question 12 (5 points)\nlisten\nthe present value of the money in your savings account is $420, and youre receiving 3% annual interest compounded monthly. what is the future value in two months?\na) $432.60\nb) $424.11\nc) $426\nd) $422.10

Answer

Explanation:

Step1: Calculate monthly interest rate

The annual interest rate $r = 3%=0.03$. The monthly interest rate $i=\frac{r}{12}=\frac{0.03}{12}= 0.0025$.

Step2: Calculate future - value after 2 months

The compound - interest formula for future value $F = P(1 + i)^n$, where $P$ is the present value, $i$ is the interest rate per period, and $n$ is the number of periods. Here, $P = 420$, $i=0.0025$, and $n = 2$. $F=420\times(1 + 0.0025)^2$. First, calculate $(1 + 0.0025)^2=(1.0025)^2=1.00500625$. Then, $F = 420\times1.00500625=422.102625\approx422.10$.

Answer:

D. $422.10$