What is the rate compounded monthly which a perpetuity will pay $600 every month if it has a present value of $96000
The present value (PV) of a perpetuity that pays out a periodic payment (PMT) is given by the formula:
\[ PV = \frac{PMT}{r} \]
where r is the periodic interest rate. In this case, you want to find the periodic interest rate (monthly compounded) which is necessary for a perpetuity to pay $600 every month if it has a present value of $96,000.
We can rearrange the formula to solve for r:
\[ r = \frac{PMT}{PV} \]
Given that PMT is $600 per month and the PV is $96,000, the formula becomes:
\[ r = \frac{600}{96,000} \]
\[ r = 0.00625 \quad \text{(This is the monthly interest rate)} \]
To express this as a percentage, we multiply by 100:
\[ r \% = 0.00625 \times 100 \]
\[ r \% = 0.625\% \quad \text{(monthly compounded interest rate)} \]
So the monthly compounded interest rate that is required for a perpetuity to pay $600 every month given a present value of $96,000 is 0.625% per month.