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<div>In this document topics covered which are Department of Accounting and Finance,M.Sc. FinanceAndM.Sc. International Accounting and Financial Studies</div><div><br /></div>
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Some straightforward questions on the use of future values and present
value factors.
Q1. a) You have £100 available today to invest for twenty years and the annual
interest rate is 8 per cent. The interest payments are to be reinvested, also
at a rate of 8 per cent. How much will you have available twenty years
from now?
20
b) Assume that the interest rate is 4 per cent rather than 8 per cent and
repeat the calculation carried out to answer part (a). [Observe the
difference in the sums available in year twenty.]
20
Sum accumulated at 4 per cent is less than 50 per cent of that built up at 8
per cent – reflects the lower interest rate and the effects of “compounding”
over time.
Q2. a) You decide to save £2,000 per annum and place the savings in a deposit
account at the end of each of the next five years. If you can invest your
savings at 12 per cent how much will you have accumulated by the end of
year five?
5
5 / 0.
b) You are given £500 today and decide to place this in a savings account
which will earn interest at 12 per cent. You decide to save £500 for each
of the next five years to add to the initial sum. How much will you have in
the savings account by the end of year five?
5
5
5 / 0.
2
alternatively: divide through by 500
5
5
= 500 x 8. 1152 = 4057. 59
Q4. a) A loan of £30,000 is to be paid back in six annual and equal instalments.
Interest of 8 per cent is charged on the outstanding balance of the loan.
Determine the annual instalments. Present value of repayments must equal
the loan at the specified interest rate.
Instalment
Loan /
Year Loan at
the start
of the
period
Interest 8%Loan at
the end
of the
period
Repayment
b) A loan of £30,000 is to be paid back in six equal instalments of
£7,297. Determine
the effective interest rate (i) on the loan.
If
Instalment = Loan / PVAF
PVAF = Loan / Instalment
and gives tables and values of PVAF and n it is possible to determine r
6 / r
Using tables
6 / r
r ≅ 12%
Year Loan at
the start
of the
period
Interes
t
Loan at
the end
of the
period
Repayment
Present Value
Q5. a) The present value annuity factor for seven years at an interest rate of 9.
per cent is 4 .9088. Determine the annuity factors for years six and eight by
adjusting the given annuity value rather than by calculating new annuity
factors from scratch.
To determine the present value annuity factor for year 6 deduct the
discount factor for 7 from PVAF ( 7 ,9.7 5 %) , ie. 4.9088 – 0.5214 = 4.3874.
To determine the present value annuity factor for year 8 add the discount
factor for year 8 to the PVAF ( 7 ,9.75%) , ie. 4 .9088 + 0.4751 = 5.3839.
b) A contract specifies that a company will received £80,000 each year for
10 years, the first payment being received three years from now. What is the present value
of these payments if the interest rate is 6 per cent?
x PVF
PV of 80 , 000 in years 3‐12 = 80, 000 x 6.5505 = 524,