# Regular Payments to Accumulate a Target Amount

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

Q. Little Miss Muffet was spending some time at the office and she found a bank account paying 6% interest annually.
She wished to make regular payments that will accumulate to $5000 over a period of five years.
How much money will she need to invest each year?

A. She will need to invest $887 each year.

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 wish to accumulate $10,000. You have two options.

Option 1 is a savings account which pays 6% interest a year for 8 years.

Option 2 is a savings account which pays 2% interest a year for 10 years.

Which option requires the lowest annual payments?

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

A. Option 1 needs an annual deposit of $1010.36 a year and Option 2 needs $913.27 a year, therefore Option 2 requires the lowest annual payments.

**Regular Payments to Accumulate a Target Amount**:

A. She will need to invest $887 each year.

This was calculated using the following annuity formula:

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

• We wish to calculate

**RP**, the regular payment you need to make •

•

**TA**, the target amount, is $5000 •

•

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

•

**n**, the number of payments is 5 •

We now put these numbers into the equation and find:

**RP**= 5000 x 0.06/[(1 + 0.06)

^{5}-1]

Therefore

**RP**= 5000 x 0.06/[1.3382256 - 1]

**Hence RP = $886.98**

Now here's a practice question for you:

Q. You wish to accumulate $10,000. You have two options.

Option 1 is a savings account which pays 6% interest a year for 8 years.

Option 2 is a savings account which pays 2% interest a year for 10 years.

Which option requires the lowest annual payments?

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

A. Option 1 needs an annual deposit of $1010.36 a year and Option 2 needs $913.27 a year, therefore Option 2 requires the lowest annual payments.