# Level annuity payable monthly

A loan of £10,000 is to be repaid over 10 years by a level annuity payable monthly in arrears. The amount of the monthly payment is calculated on the basis of an interest rate of 1% per month effective. Find the monthly repayment, the total capital repaid and interest paid in the first and last year respectively.

I've found so far that 10 years is equivalent to 120 months and using the formula $$Ra_{n \rceil} = 10000 = R\frac{1-(v)^{120}}{i}$$ Rearranged to find that R = 143.47 (ie. monthly repayment of £142.47) where i =0.01, v = $\frac{1}{1+v}$ and n = 120.

I'm struggling to find out the total capital repaid and interest paid bits though.

• One should write $$10000 = R a_{\overline{120}\rceil i} = R \frac{1 - v^{120}}{i} = R \frac{1 - (1.01)^{-120}}{0.01} = 69.7005 R,$$ which gives $R = 143.47$ (you then wrote $142.47$ in parentheses). You also write $v = 1/(1+v)$ when it should be $v = 1/(1+i)$. Oct 14, 2016 at 16:28

## 1 Answer

The total capital repaid is just the monthly payment times the number of months. The interest paid is the total capital repaid minus the amount borrowed.