R language

Suppose you are approved a home loan for $700, 000, with an annual interest rate of 5%. (Don't worry if you don't understand these terms. I'll give you the formulae you need.) You receive the money on January 1st, 2021. On the 1st of February, and every month thereafter until the loan is repaid, you make a repayment.

The amount of money that you still owe is calculated as follows, money owed today = (1 + monthly interest rate) (money owed last month) - today's repayment where monthly interest rate = annual interest rate / 12.

a. Suppose that you repay at $4400 per month. Use a loop (for, while, or repeat) to calculate the number of repayments (including the final, partial payment) you need to make to repay the loan. Show that the loan is repayed after 262 months (i.e. after 262 monthly repayments).

b.To pay the loan in exactly 25 years of monthly payments, we use the following formula,