Question

) Your bank plans to make a $20,000 loan to a customer which will have three annual installment payments. Your bank will charge 6% APR on the loan. What is the duration of this loan at the time of its origination?

Answer 1

To calculate duration of a loan we need to use the following formula:

Duration = present value of a cash flow * period / Loan amount

Loan amount is $ 20,000, annual rate of interest is 6 %. Since separate discounting factor is not given in question the rate is considered at 6%

Lets calculate present value of a cashflow * period as under:

period	cashflow	period * cashflow	present value @ 6%	Present value of cashflow
1	1200 (i.e.$20,000 *6%)	1200 (i.e. $ 1200*1)	0.94 (i.e. 1/1.06)	1128 (i.e. 1200 *0.94)
2	1200	2400 (i.e. 1200*2)	0.89 (i.e. 1/1.06*1.06)	2136 (i.e. 1200* 0.89)
3	1200	63600	0.84	53400
	Total			56,664

Duration = $56,664/$20000 = 2.83