# Annuity investment, find future value

• pbonnie
In summary, you can treat a 19 year investment as if it were a 20 year investment with an extra 2000 at the end, and you would compound it annually.
pbonnie

(attached)

## Homework Equations

Sn = (a(1-r^n))/(1-r)

## The Attempt at a Solution

This was my attempt, but I think I've done this wrong. I'm not really sure how to account for the fact that the payments are made at the end of the year. Unless that means I would act as if it were a 19 year investment?
n = 20 a = 2000 r = 8.5%/4 = 0.085/4 = 0.02125 Sn = (a(1-r^n))/(1-r)
S20 = (2000(1-〖(1+0.02125)〗^20))/(1-(1+0.02125)) S20 = 49 204.22
The final amount would be $49 204.22 #### Attachments • math.png 9.3 KB · Views: 546 Yes, you can treat it as a 19 year investment, just adding an extra 2000 at the end (no interest). But you have another problem. You have effectively quartered the interest rate. There are 80 interest periods, not 20. I suggest you first work out the equivalent interest rate for compunding annually. pbonnie said: ## Homework Statement (attached) ## Homework Equations Sn = (a(1-r^n))/(1-r) ## The Attempt at a Solution This was my attempt, but I think I've done this wrong. I'm not really sure how to account for the fact that the payments are made at the end of the year. Unless that means I would act as if it were a 19 year investment? n = 20 a = 2000 r = 8.5%/4 = 0.085/4 = 0.02125 Sn = (a(1-r^n))/(1-r) S20 = (2000(1-〖(1+0.02125)〗^20))/(1-(1+0.02125)) S20 = 49 204.22 The final amount would be$49 204.22

To second what haruspex has said: the way that financial institutions typically operate is to divide an annual (nominal) interest rate by the number of compounding periods. That makes the *actual* annual rate different from the nominal one. For example, if we are dealing with a (nominal) rate of 12% per annum, compounded monthly, the actual annual rate would be
$$r = \left( 1 + \frac{0.12}{12} \right)^{12} - 1 = .126825030 \approx 12.68\%.$$

Oh okay great, thank you both. I originally had 80 periods but I thought I was doing it wrong. So I would do 76 compounding periods, and add 2000 to the final answer?

So then the final answer to a) would be:
S19 = (2000(1-〖(1+0.02125)〗^76))/(1-(1+0.02125)) S19 = 164 772.79
The final amount would be $164 772.79 +$2000 = \$166 772.79

and b) would be:
S20 = (2000(1-〖(1+0.02125)〗^80))/(1-(1+0.02125)) S20 = 174 203.37
?

pbonnie said:
Oh okay great, thank you both. I originally had 80 periods but I thought I was doing it wrong. So I would do 76 compounding periods, and add 2000 to the final answer?

That would be doing it the hard way: the payments are yearly, while the compounding is quarterly. This mismatch makes some of the formulas harder and more intricate. If I were doing it I would just do 20 yearly periods, but I would use the "true" annual interest rate in the calculation.

Thank you :)

## 1. What is an annuity investment?

An annuity investment is a financial product that provides a series of regular payments over a set period of time. These payments can be made either in a lump sum or through a series of smaller payments.

## 2. How does an annuity investment work?

An annuity investment works by investing a sum of money in a contract with an insurance company or financial institution. The investor then receives regular payments over a set period of time, usually until retirement. The amount of these payments is determined by factors such as the initial investment, interest rates, and the length of the contract.

## 3. What is the future value of an annuity investment?

The future value of an annuity investment is the total amount of money that an investor can expect to receive from their annuity at a future date, taking into account the initial investment, interest rates, and the length of the contract. This can be calculated using a formula that takes into account the time value of money.

## 4. How can I find the future value of an annuity investment?

The future value of an annuity investment can be calculated using a formula called the future value of an annuity (FV) formula. This formula takes into account the initial investment, interest rates, and the length of the contract. Alternatively, there are many online calculators and financial planning tools that can help you calculate the future value of an annuity investment.

## 5. What are the benefits of investing in an annuity?

Investing in an annuity can provide a steady stream of income over a set period of time, making it a popular choice for retirement planning. Annuities can also offer tax-deferred growth on the investment, meaning that taxes are not paid until the funds are withdrawn. Additionally, some annuities offer a death benefit, which ensures that any remaining funds will be passed on to beneficiaries after the investor's death.

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