What is the difference between these two problems?

**Problem A** Kanye wants to save $10,000 in 5 years by making monthly payments into an ordinary annuity for a down payment on a condominium at the shore. If the annuity pays **0.80% annual interest **compounded monthly, what will his monthly payment be?

VS.

**Problem B** Kanye wants to save $10,000 in 5 years by making monthly payments into an ordinary annuity for a down payment on a condominium at the shore. If the annuity pays **0.80% monthly interest** compounded monthly, what will his monthly payment be?

The key is to notice that the interest rate can be given as an annual rate or a monthly rate. How do we apply the annuity formula,

In this formula,

*A*: future value

*R*: payment

*m*: number of times interest is compounded in a year

*r*: annual interest rate

*n*: number of compounding periods

To help us see the difference, think of * ^{r}*/

*as the interest rate per period. In Problem A, the annual interest rate is 0.80% and interest is compounded 12 times a year. To solve this problem, we set r = 0.008 and m = 12 and put the other numbers in:*

_{m}The fraction on the right is equal to 61.19535446.

Solving for R in this equation gives R ≈ 163.41.

In Problem B, the interest rate given to you is the interest rate per period. In other words, ^{r}/_{m} = 0.008 This means that in this problem, you need to solve for *R* in

In this case, the fraction is equal to 76.62386683:

Dividing this number into 10,000 gives a payment of *R* ≈ 130.51.