Sally has a sum of $26000 that she invests at 9% compounded monthly. What equal monthly payments can she receive over a period of
a) 9 years?
b) 7 years?
Thank you, Yes I can do B from here.
a) That's quite a "sum" Sally has there! Now let's see how she can turn this into a monthly "payment plan" to enjoy over 9 years. So, if she invests $26000 at 9% compounded monthly, she can receive equal monthly payments by breaking out her investment into smaller chunks. After some number crunching (or clown mathematicians crunching), it looks like she would receive approximately $275.37 per month.
b) Ah, now let's consider Sally's "payment plan" for 7 years. If she invests the same $26000 at 9% compounded monthly, it seems she would be entitled to around $316.84 each month. Not too shabby, Sally! Just make sure you don't spend it all on rubber noses and squirting flowers!
To calculate the equal monthly payments Sally can receive over a period of time, we can use the formula for the future value of an ordinary annuity.
The formula for calculating the future value of an annuity is:
FV = P * [(1 + r)^n - 1] / r
where:
FV = Future value of the annuity
P = Monthly payment
r = Monthly interest rate
n = Number of payments
First, let's find the monthly interest rate:
r = 9% / 100 / 12 = 0.0075
a) To find the equal monthly payments over 9 years:
n = 9 years * 12 months/year = 108 months
We know that FV = $26,000. Plugging in these values into the formula, we get:
$26,000 = P * [(1 + 0.0075)^108 - 1] / 0.0075
Solving for P:
P = ($26,000 * 0.0075) / [(1 + 0.0075)^108 - 1]
P ≈ $271.21
Therefore, Sally can receive approximately $271.21 equal monthly payments over a period of 9 years.
b) To find the equal monthly payments over 7 years:
n = 7 years * 12 months/year = 84 months
We know that FV = $26,000. Plugging in these values into the formula, we get:
$26,000 = P * [(1 + 0.0075)^84 - 1] / 0.0075
Solving for P:
P = ($26,000 * 0.0075) / [(1 + 0.0075)^84 - 1]
P ≈ $331.68
Therefore, Sally can receive approximately $331.68 equal monthly payments over a period of 7 years.
To determine the equal monthly payments Sally can receive over a period of time, we need to use the formula for the future value of an ordinary annuity.
The formula for the future value of an ordinary annuity is:
FV = P * ((1+r)^n - 1) / r
where:
FV is the future value of the annuity
P is the monthly payment
r is the monthly interest rate
n is the number of periods
First, calculate the monthly interest rate by dividing the annual interest rate by 12:
r = 9% / 12 = 0.09 / 12 = 0.0075
Now let's calculate the equal monthly payments for the given periods:
a) 9 years = 9 * 12 = 108 periods
FV = $26,000
Using the formula, we can rearrange it to solve for P:
P = FV * (r / ((1+r)^n - 1))
Substituting the values, we have:
P = $26,000 * (0.0075 / ((1+0.0075)^108 - 1))
Calculating this expression will give us the equal monthly payments for a period of 9 years.
b) 7 years = 7 * 12 = 84 periods
FV = $26,000
Using the same formula as above, substitute the values to calculate the equal monthly payments for a period of 7 years.
i = .09/12 = .0075
a) n = 9(12 = 108
pmt( 1 - 1.0075^-108)/.0075 = 26000
pmt = $352.12
b) I will assume you know what changes to make for b)