# Determining the interest rate necessary to retain a certain balance after sixty monthly withdrawals [closed]

I have seen many examples online for "Time Value Money" and "sinking funds". I want to know how I can combine any type of solver in the PMT-PV equation? Because all these examples have known FV, PV, and i (interest rate) and they all solve for PMT, but I want to solve for i.

Example: I have 10 million in the bank account, and I want to have 5 million in the balance of the account after 5 years. I want to make a withdrawal of 100 thousand every month (end of month), so I have to know what interest rates I am seeking for so this would work for me.

Any help?

## closed as unclear what you're asking by mhoran_psprep, Dheer, JoeTaxpayer♦Jan 29 '17 at 20:15

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## 1 Answer

You need to solve the money-weighted return equation. It cannot be expressed as a formula for the interest, but it can be solved numerically as shown here.

Using the OP's figures, with monthly withdrawals of \$100,000.

The summation for the withdrawals can be replaced with the standard annuity formula. The resulting monthly return is converted to a nominal annual return compounded monthly.

Money-weighted return equation with start and end balances `s0` and `s1` The interest is 2.63282 % per annum, nominal compounded monthly.

Selectable equation

``````10000000 - (100000 - 100000 (1 + x)^-60)/x - 5000000/(1 + x)^60 = 0
`````` 