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?
What is
1000(1.06^4) + 1100(1.06^3) + 680(1.06) ?
To solve this problem, we need to calculate the future value of each deposit and then add them together to find the total amount in the account.
The formula for calculating the future value of an investment with compound interest is:
Future Value = Principal * (1 + (Interest Rate / Compound Frequency))^(Compound Frequency * Time)
Let's start by calculating the future value of each deposit:
First deposit:
Principal = $1,000
Interest Rate = 12% (0.12)
Compound Frequency = Semi-annually (2 times per year)
Time = 2 years
Future Value of the first deposit:
FV1 = $1,000 * (1 + (0.12 / 2))^(2 * 2)
= $1,000 * (1 + 0.06)^4
= $1,000 * (1.06)^4
≈ $1,000 * 1.262476
≈ $1,262.48
Second deposit:
Principal = $1,100
Interest Rate = 12% (0.12)
Compound Frequency = Semi-annually (2 times per year)
Time = 1.5 years
Future Value of the second deposit:
FV2 = $1,100 * (1 + (0.12 / 2))^(2 * 1.5)
= $1,100 * (1 + 0.06)^3
= $1,100 * (1.06)^3
≈ $1,100 * 1.191016
≈ $1,310.12
Third deposit:
Principal = $680
Interest Rate = 12% (0.12)
Compound Frequency = Semi-annually (2 times per year)
Time = 0.5 years
Future Value of the third deposit:
FV3 = $680 * (1 + (0.12 / 2))^(2 * 0.5)
= $680 * (1 + 0.06)^1
= $680 * (1.06)^1
≈ $680 * 1.063
≈ $723.04
Now, we can find the total amount in the account by adding up the future values of all deposits:
Total Amount = FV1 + FV2 + FV3
= $1,262.48 + $1,310.12 + $723.04
≈ $3,295.64
Therefore, the total amount in the account now is approximately $3,295.64.