Question

In 6 years Harry and Sally would like to have $28,000.00 for a down payment on a house. How much should they deposit each month into an account paying 5% compounded monthly?

Answer 1

Derivation of formula: Suppose they should deposit each month. With one month's interest on the first month's , the deposit becomes

Now this amount will accumulate interest for years, or months, hence, after months, the deposit owing to just first month's amount becomes

The next month's will accumulate interest for months, so owing to this next month's the deposit amount after years becomes

Similarly for each month. The last month's will have interest for just one month, so this becomes

Thus, if they deposit every month for years then the total amount will be

This total has to be , which means

Therefore, they must deposit each month.