a savings account pays 2% interest compounded...
a savings account pays 2% interest compounded annually. if $1,200 is deposited initially and again at the first of each year, how much money will be in the account three years after the initial deposit? $1,248.48 $2,472.48 $3,672.48 $3,745.93
Answer
# Explanation:
## Step1: Calculate the future - value of the first deposit
The compound - interest formula is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years. For the first $P_1=1200$ deposit, $r = 0.02$ and $n = 3$. So $A_1=1200(1 + 0.02)^3=1200\times1.02^3=1200\times1.061208 = 1273.45$.
## Step2: Calculate the future - value of the second deposit
The second $P_2 = 1200$ deposit is made at the start of the second year, so it earns interest for 2 years. Using the compound - interest formula, $A_2=1200(1 + 0.02)^2=1200\times1.0404 = 1248.48$.
## Step3: Calculate the future - value of the third deposit
The third $P_3 = 1200$ deposit is made at the start of the third year, so it earns interest for 1 year. Using the compound - interest formula, $A_3=1200(1 + 0.02)^1=1200\times1.02 = 1224$.
## Step4: Calculate the total amount in the account
The total amount $A=A_1 + A_2+A_3=1273.45+1248.48 + 1224=3745.93$.
# Answer:
D. $3,745.93$