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(a) Calculate the interest on the instalment of the third year, deduct interest from this
instalment. The resulting figure is the outstanding cash price at the time of third
(last) instalment.
(b) Add the cash price calculated under (a) above to the instalment amount of the second
year, then calculate the interest on the sum so obtained and subtract it from the total
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amount due at the end of’ the second year to get the outstanding cash price at the
time of second instalment.

(c) Add the cash price calculated under (b) above to the instalment amount of the first
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year, and calculate the interest on the sum so obtained. Deduct the amount of interest
from the total amount due at the end of the first year; the result figure is the cash
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price due at the time of the first instalment
(d) Add the cash price calculated under (c) above to the down payment, if any. Then,
sum obtained will be the cash price.

The following Example 8.5 demonstrates how to calculate cash without the use of an
annuity table:
Example 8.5
Lucy Garments Ltd. purchased a sewing machine on 1 January 2021 on hire purchase
st
basis for an interest of 5 per cent. The hire purchase price was TZS 5,000,000 Payable
as follows:

Period Down payment Instalments
TZS TZS
1 930,000 1,426,000

2 - 1,804,000
3 - 840,000
Required: Calculate the cash price of the sewing machine and interest paid with each
instalment.

Solution 8.5
TZS Interest

Total amount due on 3 instalment (last) 840,000
rd
Less: interest (40,000) 840 ,000 # 5 = 40,000
105
Outstanding cash price on 3 instal- 800,000
rd
ment

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