Deposits of $1,000, $1,100 and $680 were made into a savings account, the first two years ago, the second 18 months ago, the third 6 months ago. How much is in the account now if the interest on all deposits is 12% compounded semi-annually?
To find out how much is in the account now, we need to calculate the compounded interest on each deposit and sum them up.
First, let's calculate the compounded interest on the first deposit of $1,000 made two years ago.
The interest rate is 12% compounded semi-annually, so the effective interest rate for each compounding period is 12%/2 = 6%.
The time period for the first deposit is 2 years, which is equivalent to 4 compounding periods (2 years * 2 compounding periods per year).
To calculate the final amount, we can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
where:
FV = Final Value
PV = Present Value (initial deposit)
r = interest rate per period (as a decimal)
n = number of compounding periods per year
t = number of years
For the first deposit:
FV1 = 1000 * (1 + 0.06/2)^(2*2)
FV1 ≈ 1000 * (1.03)^4
FV1 ≈ 1000 * 1.1255
FV1 ≈ $1,125.50
Next, let's calculate the compounded interest on the second deposit of $1,100 made 18 months ago.
The time period for the second deposit is 1.5 years, which is equivalent to 3 compounding periods (1.5 years * 2 compounding periods per year).
For the second deposit:
FV2 = 1100 * (1 + 0.06/2)^(2*1.5)
FV2 ≈ 1100 * (1.03)^3
FV2 ≈ 1100 * 1.0927
FV2 ≈ $1,201.97
Lastly, let's calculate the compounded interest on the third deposit of $680 made 6 months ago.
The time period for the third deposit is 0.5 years, which is equivalent to 1 compounding period.
For the third deposit:
FV3 = 680 * (1 + 0.06/2)^(2*0.5)
FV3 ≈ 680 * (1.03)^1
FV3 ≈ 680 * 1.03
FV3 ≈ $700.40
Now, let's sum up the final values of all three deposits to find the total amount in the account now:
Total Amount = FV1 + FV2 + FV3
Total Amount ≈ 1125.50 + 1201.97 + 700.40
Total Amount ≈ $3,027.87
Therefore, the total amount in the account now is approximately $3,027.87.