# The Future Value of Regular Payments

On the Annuity Formula homepage, we used the following example to introduce:

Q. Billy the Annuity Kid invests $1000 at the end of each year for ten years.
His investment pays a return of 6% a year.
How much money will Billy have saved including interest at the end of year ten?

A. The value of Billy's annuity at the end of year ten is $13,180.79.

This was calculated using the following annuity formula:

• We wish to calculate

•

•

•

We now put these numbers into the equation and find:

Therefore

Now here's a practice question for you:

Q. You invest $10,000 a year. Compare how much money you will have accumulated after 20 years in Fund A, paying an annual return of 5%, with Fund B, paying an annual return of 10%. (All returns are reinvested.)

Try doing the calculation yourself, then scroll down to check your answer at the bottom of the page.

A. After 20 years, Fund A will be worth $33,066 and Fund B will be worth $57,275. Fund B is worth $24,209 more than Fund A. A few percentage points on your interest rate makes a big difference over long enough time.

**The Future Value of Regular Payments**:

A. The value of Billy's annuity at the end of year ten is $13,180.79.

This was calculated using the following annuity formula:

**Using the annuity formula to answer the question:**

• We wish to calculate

**FV**, the future value •

•

**RP**, the regular payment, is $1000 •

•

**i**, the interest rate, is 6%, which we write as 0.06 •

•

**n**, the number of payments is 10 •

We now put these numbers into the equation and find:

**FV**= 1000 x [(1 + 0.06)

^{10}- 1]/0.06

Therefore

**FV**= 1000 x [1.790848 - 1]/0.06

**Hence FV = $13,180.79**

Now here's a practice question for you:

Q. You invest $10,000 a year. Compare how much money you will have accumulated after 20 years in Fund A, paying an annual return of 5%, with Fund B, paying an annual return of 10%. (All returns are reinvested.)

Try doing the calculation yourself, then scroll down to check your answer at the bottom of the page.

A. After 20 years, Fund A will be worth $33,066 and Fund B will be worth $57,275. Fund B is worth $24,209 more than Fund A. A few percentage points on your interest rate makes a big difference over long enough time.