Angie needs to have $15,000 at the end of 6 years. How much should she deposit weekly into an ordinary annuity if it earns 6.5% interest compounded weekly?
This time you want future amount
i = .065/52 = .00125
P( 1.00125^312 - 1)/.00125 = 15000
...
P = 39.34
weekly payment is $39.34
To determine how much Angie should deposit weekly into an ordinary annuity, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value
P = Weekly deposit
r = Interest rate per period
n = Number of periods
In this case, Angie needs to accumulate $15,000 in 6 years. The interest is compounded weekly at a rate of 6.5%.
First, let's convert the interest rate to a decimal:
r = 6.5% = 0.065
Next, let's determine the number of compounding periods:
Since the interest is compounded weekly, and there are 52 weeks in a year, the total number of compounding periods is:
n = 6 years * 52 weeks/year = 312
Now, we can substitute the values into the formula and solve for P (the weekly deposit):
15,000 = P * [(1 + 0.065)^312 - 1] / 0.065
To solve this equation, we can use algebraic manipulation:
Multiply both sides of the equation by 0.065:
15,000 * 0.065 = P * [(1 + 0.065)^312 - 1]
975 = P * [(1.065)^312 - 1]
Divide both sides of the equation by [(1.065)^312 - 1]:
P = 975 / [(1.065)^312 - 1]
Calculating this value:
P ≈ $15.05
Therefore, Angie should deposit approximately $15.05 weekly into the ordinary annuity to accumulate $15,000 at the end of 6 years, with a 6.5% interest rate compounded weekly.