IENG112
Problem Sheet No. 5
Solutions
1. The original value of equipment KX100 is 8000 USD. The law says that the yearly
depreciation is 12.5 percent. What is the yearly cost of KX100 in the overhead?
Solution. The yearly depreciation is 12.5 percent of the purchase price. Thus the yearly cost in the
overhead of KX100 is 8000 x 0.125 = 1000 USD.
2. The sum of the bank loan is 10,000 USD. The interest rate is 10 percent. The loan must be
paid back in one shot after two years. What is the nominal value of the amount what must be
paid at that time?
Solution. The bank charges interest at the end of the first year and once more at the end of the
second year. The debt at the end of the first year becomes 10,000 x 1.1 = 11,000 USD. It
becomes 11,000 x 1.1 = 12,100 USD at the end of the second year. This is the sum you must pay.
In general, if you pay only after n year then you must pay 10,000 x 1.1n USD.
3. What is the net present value of 10,000 if it is paid in 2018 and the interest rate is 5 percent?
Solution. The amount in question is paid three years later. Thus, NPV = 10,000/1.053=8638.4
USD.
4. How much should be saved at the end of each year of a period of 8 years if the future value is
10,000 and the interest rate is 4 percent?
Solution. The formula what you should apply is
(1 + 𝑖)𝑛+1 − 1
𝐿=𝑦
𝑖
Where L is the total saved value (target value), y is the yearly installment, i is the interest rate, and
n the number of years that the first installment obtains interest. If the first installment is paid at the
end of the first year then n=7 and the equation becomes
10000 = 𝑦
Hence y=1085.3.
1.048 − 1
= 9.2142𝑦.
0.04
5. What is the yearly installment of a loan of 1200 USD if it is paid back in 6 years and the
interest rate is 6 percent?
Solution. The formula which must be applied here is
(1 + 𝑖)𝑛 𝐿 = 𝑦
(1 + 𝑖)𝑛 − 1
𝑖
Hence the equation
1.066 − 1
1.06 × 1200 = 𝑦
0.06
6
is obtained which gives y=244 USD.
6. How much is the loan if the yearly installment is 1000 USD in a period of 5 years and the
interest rate is 7?
Solution. Again the same formula must be applied. This time the unknown quantity is L. The
equation becomes in the form
1.075 × 𝐿 = 1000
1.075 − 1
0.07
Hence L=4100.
7. You get a loan of 8000 batka. The interest rate what you have to pay is 10 percent. You must
pay back the loan in 4 years. What is the yearly installment?
Solution. You must proceed in the same way as in Problem 5. The current form of the equation is
1.14 × 8000 = 𝑦
1.14 − 1
.
0.1
Hence y=2523.8.
8. You put 10,000 batka in a bank of Noname country at the end of each year of a period of 20
years starting with the end of the 0-th year. The yearly interest rate paid by the bank is 5
percent. You keep your money in the bank during the period of 20 years. How much do you
own at the end of the period?
Solution. This problem is similar to Problem 4, that is the same formula must be applied. Its
current form is
𝐿 = 10000
1.0521 − 1
= 357192.5
0.05