Annuities: Determining the Interest Rate

[Itachi]

Annuities: Determining the Interest Rate (help needed!)

David has $2000 to invest in an annuity. What interest rate must be obtain in order to receive payments of $500 at the end of each year for the next 5 years?

 

[Mark]

Im assuming youv'e been given some sort of financial math equation to solve these types of problems. I learned them in grade 11 math... here is the equation...

http://oakroadsystems.com/math/pics/loaneq5.gif

you just put the numbers in...

 

[M98Ranger]

To determine the interest rate needed to receive payments of $500 for the next 5 years, we can use the formula for present value of an annuity:

PV = PMT x [(1 - (1 + r)^-n)/r]

Where:
PV = present value (in this case, $2000)
PMT = payment amount ($500)
r = interest rate
n = number of periods (in this case, 5 years)

Plugging in the given values, we get:

$2000 = $500 x [(1 - (1 + r)^-5)/r]

Next, we need to solve for r. This can be done by trial and error or by using a financial calculator or spreadsheet. Using a financial calculator, we can input the values and solve for r, which in this case is approximately 9.22%.

Therefore, in order to receive payments of $500 for the next 5 years, David would need to obtain an interest rate of approximately 9.22%. It's important to note that this is the minimum interest rate needed, so if David is able to obtain a higher interest rate, he will receive more than $500 in payments each year.

 

[M98Ranger]

To determine the interest rate needed for this annuity, we can use the formula for present value of an annuity:

PV = PMT * [(1 - (1 + r)^-n)/r]

Where:
PV = present value (in this case, $2000)
PMT = payment amount ($500)
r = interest rate
n = number of periods (in this case, 5 years)

Substituting in the given values, we get:

$2000 = $500 * [(1 - (1 + r)^-5)/r]

Simplifying the equation, we get:

4 = (1 - (1 + r)^-5)/r

Multiplying both sides by r, we get:

4r = 1 - (1 + r)^-5

Adding (1 + r)^-5 to both sides, we get:

4r + (1 + r)^-5 = 1

Using a financial calculator or spreadsheet, we can solve for r, which gives us an interest rate of approximately 7.96%. This means that if David invests $2000 in an annuity with an interest rate of 7.96%, he will receive payments of $500 at the end of each year for the next 5 years.