TimeValue of Money Part 3 solved questions with solutions
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14.
TCS wants to offer scholarship of 35000 per year to 100 disabled sports
persons starting from one year now for
next 10 years and it will increase at a constant rate of 5% every year Find the
present value of this scholarship if rate of interest is 7%.
Solution:
Present value of Annuity with constant growth rate = [Cash flow 1 ÷ (r-g) ] × [
1- { (1+g) ÷(1+r)}n ]
=
[Cash flow 1 / (r-g) ] × [ 1- { (1+g) /(1+r)}n ]
=
=
Rs. 17,
50, 000 × (1- 0.981310)
=
Rs. 17,
50, 000 × (1- 0.828) = Rs. 3,00, 917
Present value of scholarship given to 100 disabled sports
persons for 10 years= Rs.3, 00,917 × 10 = Rs. 3, 00, 91, 700
15.
A machinery is to be replaced after 7 years which will cost Rs. 10, 00, 000 at the
end of 7 years. However, Rs. 75,000 can be realized by selling the existing
machinery at that time. Calculate the amount to be deposited every year to get
the amount required to purchase new machinery after 7 years considering deposityields a rate of 6 %.
Solution:
Replacement cost of machinery at the end of 7 year after
deducting realized value of existing machinery = Rs. 10, 00, 000 – Rs. 75, 000
= Rs. 9, 25, 000
Future value of Annuity = Annuity × FVAF0.06, 7
→ Annuity = FV/ FVAF0.06, 7 = Rs. 9, 25, 000 /
8.394 = Rs. 1, 10, 198
Amount to be deposited every year to get Rs. 9, 75, 000 at
the end of year 7 Rs. 1, 10, 198.
16.
Mahesh took a loan of Rs. 15, 00,000 to be paid in ten equal annualinstallments at rate of 15 %. Calculate annual installment payable by him.
Solution:
PV of annuity = Annuity × PVAF 0.15, 10 =>
Annuity = PV of annuity / × PVAF 0.15, 10
Annuity / Annual installment = Rs. 15, 00,000 /5.019 = Rs. 2,
98,864
17.
A financial institution offered that it will pay a lump sum amount of Rs.
12,000 at the end of 10 years to investors who pay 1,000 annually for 10 years.
Find out implicit rate of interest in the offer.
Solution: FV = Annuity × FVAF r, 10
=> FVAF r, 10 = FV/Annuity = Rs. 12,000 /Rs. 1,000
= 12
Looking into FVAF table at 10 years, implicit rate of
interest is 4 %.
18.
SBI has issued deep discount bonds of Rs. 15,000 each which will mature after 7
years for 35,000. What is implicit rate of interest of these DDRBs.
Solution:
FV = PV × (1+r) 7 => (1+r) 7 = FV /
PV = Rs. 35,000 / Rs. 15,000 = 2.333
=> (1+r) 7 = FVPr, 7 = 2.333
1+r = (2.333)
1 + r = 1.1284
S0, r = 1.1284 – 1 =0.1284 = 12.84 %
19. Profit of Tesla has grown from Rs. 10
crores to Rs. 100 crores in 5 years’ time. Calculate compound rate of growthcompany has maintained in profit during this period. Assume that profit has
grown evenly throughout this period.
Solution:
Growth rate = (FV/PV) 1/5 - 1 = (100/10)
1/5 - 1 = 1.5849 – 1 = 0.5849 = 58.49 %
20. Find the number of years required toaccumulate a sum of Rs. 5,000 with an initial investment of 1,200 at 10% rate
of interest.
Solution:
FV = PV × (1+r) n PV × FVF0.1, n
FVF0.1,
n or (1+r)
n = Rs. 5000 / Rs. 1200 = 4.17
(1.1) n = 4.17
Looking at FVF table at 10 % no. of years for value
of 4.17 is close to 15 years
So, n = 15 years
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