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A simple financial math problem:

Mack obtains $500\ 000$ repayable over $20$ years. If interest is compounded monthly at $9.25\%$ per annum, determine the monthly repayments if the repayment begins in $6$ months time.

I used the formula:

$$P_v = x[(1-(1+i)^{-n})/i]$$

but I'm not getting the right value.

What am I doing wrong?

TMM
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Daniel Feinstein
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    What you are doing wrong is depending on formulas, when you should be understanding how the formula is derived and using that understanding to do the problem. Other possibilities are that you are plugging in the wrong values for the variables, or misusing your calculator --- it's hard to tell what you have done wrong, when you don't show us what you have done! – Gerry Myerson May 29 '13 at 12:53
  • im sorry i havnt been taught this topic yet – Daniel Feinstein May 29 '13 at 13:23
  • What is the "right" value? – DJohnM May 29 '13 at 19:47

1 Answers1

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Because repayment begins in $6$ months, the effective principal is

$$P = 500,000\, \left ( 1 + \frac{i}{12} \right )^6$$

where $i=0.0925$ is the annual interest rate. The monthly payment is then

$$m = \frac{P \, (i/12)}{1-\left [ 1 + (i/12) \right ]^{-240}}$$

Plugging in the numbers, I get a monthly payment of about $\$4795.25$.

Ron Gordon
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  • why do you times P by (i/12)? – Daniel Feinstein May 29 '13 at 13:54
  • @DanielFeinstein: refer to the equation for determining monthly payment from principal, interest rate, and number of compounding periods. The effective interest rate is not $i$, but $i/12$ because the month, not the year, is the compounding period. – Ron Gordon May 29 '13 at 13:55
  • @Ron Gordon Please check the numeric value $4795.25$. I've computed

    $m=500000(1+\frac{0.095}{12})^{6}\frac{\frac{0.095}{12}}{1-\left( 1+\frac{0.095}{12}\right) ^{-240}}=4886.5.$

     – Américo Tavares May 29 '13 at 15:17
  • @AméricoTavares: $i=0.0925$, not $0.095$. – Ron Gordon May 29 '13 at 15:22
  • @RonGordon Stupid mistake of mine! Sorry. – Américo Tavares May 29 '13 at 15:33
  • This is the formula for an ordinary annuity, where payments are made at the end of each period. Assuming the 500 000 is obtained on Jan 1, 2000, this solution has the first payment on July 31, 2000. Is that what was intended by the OP? – DJohnM May 29 '13 at 16:59
  • @User58220: As the OP has pleaded ignorance of the subject, who knows what he intended? My solution answers the question he posed: the formula determines the monthly payment from a loan of given principal, interest rate, and temporal extent. So assuming he obtains the loan on 1/1/2000 and interest compounds at the end of each month, then we assume that Mack makes his first payment after 6/30/2000 and before 7/31/2000, as on that date, the 7th compounding event takes place. – Ron Gordon May 29 '13 at 17:08