21.Ogden wants to save for a trip to Australia. She will need $12,000 at the end of four years. She can invest a certain amount at the beginning of each of the next four years in a bank account that will pay her 6.8 percent annually. How much will she have to invest annually to reach her target?
Set BGN
2,538
To find out how much Ogden needs to invest annually to reach her target of $12,000 at the end of four years, we can use the concept of future value of an ordinary annuity.
The formula to calculate the future value of an ordinary annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Annual investment amount
r = Interest rate per period
n = Number of periods
In this case, Ogden wants to save for four years and the interest rate is 6.8 percent annually.
We can plug in the values into the formula and solve for P (annual investment amount):
12000 = P * [(1 + 0.068)^4 - 1] / 0.068
First, let's simplify the formula:
1.068^4 - 1 = 0.315972
Now, rearrange the formula to solve for P:
12000 = P * 0.315972 / 0.068
Multiply both sides of the equation by 0.068:
816 = P * 0.315972
Divide both sides of the equation by 0.315972:
P ≈ 816 / 0.315972
P ≈ $2,584.76
Therefore, Ogden will need to invest approximately $2,584.76 annually to reach her target of $12,000 at the end of four years.