Hire Purchase Actuarial Method

May 10, 2012
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Two companies enter into a hire purchase agreement whereby the seller will hire to the buyer one item of plant with a fair value of £10,000. The period of the agreement is 5 years with a rental of £2960 per annum payable in advance.
Assume that the actuarial method using an interest rate of 25% is adopted for allocating the finance charges over the HP agreement.

Question is show how the finance charges would be allocated over the HP agreement.

Can any one provide me with some information on what is meant by the actuarial method and if possible some examples to illustrate this.

Thanks in advance.



VIP Member
Feb 12, 2012
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Actuarial method means that the interest is based on the loan outstanding amount
after the annual payment you've made. The interest rate applied in this method
is also called the "effective interest rate".

Firstly, you should compute the "Present Value" (PV) of the Hire Purchase lease
for the plant, the present value is equal to the costs of the plant that you pay
for it at the present time (In other words, you would not need to pay the hire purchase interest if you buy the plant by cash right now).

Since the annual payment for the HP lease is paid in advance, so the full amount of the
1st annual payment is used to repay the HP Loan (it is also called the "Down payment")
In other words, there is no interest shall be paid in the 1st annual payment

We can use this formula to compute the present value of the HP lease if
the payment is made at the beginning of the annuity
PV of an annuity = A + {A [ 1- (1 + i)^-(n-1)] / i}
Where A = Annual rental payment i = annual interest rate
n = no. of years

PV for the HP Lease for the plant = 2960 + {2960[ 1- (1 + 25%)^-(5-1)] / 25%
= $9,950.34 => which is nearly closed to Fair value

The following table indicates how the finance charges would be allocated over the HP agreement.

HP Lease liablity : $9,950.34
Annual Interest rate : 25.00%
Annual rental payment : $2,960.00

Principal Interest Annual
Year Opening bal Repayment Payment Payment Closing
0 9,950.34 2,960.00 - 2,960.00 6,990.34
1 6,990.34 1,212.42 1,747.58 2,960.00 5,777.92
2 5,777.92 1,515.52 1,444.48 2,960.00 4,262.40
3 4,262.40 1,894.40 1,065.60 2,960.00 2,368.00
4 2,368.00 2,368.00 592.00 2,960.00 -
----------- ---------- ----------
Total $9,950.34 $4,849.66 $14,800.00
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