# Problems with Money Weighted Rate of Return [closed]

The market value of a small pension fund’s assets was 2.7m on 1 January 2000 and 3.1 m on 31 December 2000. During 2000 the only cash flows were:

• Bank interest and dividends totalling 125,000 received on 30 June

• A lump sum retirement benefit of 75,000 paid on 1 May

• A contribution of 50,000 paid to the fund on 31 December

Show that the MWRR is 16%

What I have tried:

$3.1*10^{6}*(1+i)^{-12}-75,000*(1+i)^{-5}+50,000*(1+i)^{-12}-2.7*10^{6}=0$

solving this in wolfram alpha we get $i=0.0107371$, converting this from a monthly interest rate we find that MWRR is 13.7% which is $\neq 16$%.

Can someone please explain/show me where I went wrong in my attempted solution of the problem?

In Wolfram Alpha language ...

2.7∗10^6*(1+x)^12 -75000*(1+x)^8 +50,000 -3.1∗10^6 = 0

... gives x≈0.0124671 per month, which is 16.03% per annum.

I.e. All incomings and outgoings must add up to zero, after adjusting for the monthly interest rate "x" over the number of months invested.

• 2.7m remains in the fund for the full 13-1 = 12 months, and would normally be positive;
• 75k benefit is "missing" for 13-5 = 8 months, and is therefore negative;
• 50k incoming is positive, but does not remain in for any length of time, so the exponent is 0
• 3.1m is the final value, and is negative because it is transferred out at the end of the period.

Thanks for showing that Wolfram Alpha handles polynomials so well. Seeing that, my New Year's resolution is use it more !