An equipment can be purchased at $3,500 by cash, or through a payment plan that requires...

An equipment can be purchased at $3,500 by cash, or through a payment plan that requires an initial down payment of $1,200, and 24 end-of-month payments of $110. At what effective interest rate are these terms equivalent?

Expert Solution

Cash purchase price		$ 3,500.00
Credit purchase option
Down payment	$ 1,200.00
Installment ($110*24 month)	$ 2,640.00
		$ 3,840.00
Excess amount charged in 2 year		$ (340.00)

Equivalent rate must be where $3,500= PV of $3,840
We have to calculate IRR for the same.

Now, say IRR is 12% p.a. i.e.1% p.m.
Present value= $110PVIF+$1200PVAF
Present value= $11021.2434+$12001= $3,536.77

Now, say IRR is 14% p.a. i.e.1.167% p.m.
Present value= $110PVIF+$1200PVAF
Present value= $11020.8269+$12001= $3,490.96

IRR as per interpolation method=12%+(3536.77-3500)/(3535.77-3490.96)*(14%-12%)
IRR as per interpolation method=12%+(0.80272)*(2%)= 12%+1.6054%= 13.6054%

Effective interest rate is 13.6054% per annum or 1.13% per month at which these terms are equivalent

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ekkarill92 answered 2 years ago

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