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# 1Time Value of Money solved questions pdf Financial Management notes with solved problems pdf time value of money formula tvm solved problems time value of money illustrations with solutions pdf

1. Time Value of Money Part 1 numerical with solutions

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1. Mr. X invested Rs. 7, 10,000 atthe beginning of the year one at the rate of 10% compounded annually. Calculate how much he will receive after the end of 1st, 2nd and 3rd year of his investment?

Future value at the end of year 1 FV₁ = PV (1+r)¹= 710000 * (1+0.1)¹ = 710000 * 1.1= 781000

Or FV₁= PV × FVF_{r, n} = 710000 × PVF_.1,
1 = 710000 × 1.1 = 781000

A	B	A × B
Present value at year 0	FVF_r,n ( r= 0.1, n=1,2,3) taken from PVF table	Future Value at the end of
Rs. 7,10,000	FVF_{0.1, 1} = 1.1	Year 1 - FV₁= PV × FVF_{0.1, 1} = Rs. 7,10,000 × 1.1 = Rs. 7,81,000
Rs. 7,10,000	FVF_{0.1, 2} = 1.21	Year 2 - FV₂= PV × FVF_{0.1, 2} = Rs. 7,10,000 × 1.21 = Rs. 8,59,100
Rs. 7,10,000	FVF_{0.1, 3} = 1.33	Year 3 - FV₃ = PV × FVF_{0.1, 3} = Rs. 7,10,000 × 1.33 = Rs. 9,65,600

2. Mr. X invested Rs. 1,000, Rs. 2,000 and Rs. 5,000 at the starting of 1st, 2nd and 3rd year. What will be compounded value of his investment at the end of 3rd year when interest is provided at the rate of 12%.

Solution:

Method 1			Method 2
A	B	C = A × B	FV = PV × (1+ r)ⁿ
Money invested at the beginning of year	FVF_r,n
1- Rs. 1000	FVF _{0.12, 3} = 1.405	Rs. 1000×1.405= Rs. 1,405	= Rs. 1000× (1+ .12)³= Rs. 1,405
2 - Rs. 2000	FVF _{0.12, 2} = 1.254	Rs. 2000×1.254= Rs. 2,508	= Rs. 2000× (1+ .12)²=2,508
3 - Rs. 5000	FVF _{0.12, 1} = 1.120	Rs. 5000×1.120= Rs. 5,600	= Rs. 5000× (1+ .12)¹ = 5,600
compound value of his investment at the end of 3rd year when interest is provided at the rate of 12%		1405 + 2508 + 5600 = Rs. 9513	1405 + 2508 + 5600 = Rs. 9,513

3. Mr. X has invested an amount of Rs.15,000 each at the end of 1st, 2nd and 3rd year. Calculate the compound value of his investment at the end of 3rd year if interest is provided at a rate of 9 % compounded annually.

Solution:

FV at the end of year 3 = Annuity × FVAF _{0.09, 3} = Rs. 15,000 × 3.278 = Rs. 49,170

4. A has invested Rs. 7,000 for 3 years at an interest rate of 12 % per annum compounded semiannually. What amount he will get after 3 years?

Solution:

FV = PV × FVF_{0.06, 6} = Rs. 7,000 × 1.419 = Rs. 9,933

(In case of semiannual compounding divide r by 2 and multiply n by 2)

5. Vitthal has invested Rs. 25, 000 now for 3 years at the rate of 8 % per annum compounded quarterly. What amount he will get after 3 years?

Solution: FV = PV × FVF_{0.02, 12} = Rs. 25,000 × 1.268 = Rs. 31,700

(In case of quarterly compounding divide r by 4 and multiply n by 4)

6. Ravi wants to deposit Rs. 10, 00,000 in a bank for a year. He has received following offers of rate of interest from different banks

SBI-10.75% p.a. compounded weekly

PNB-11% p.a. compounded monthly

HSBC-11.25% p.a. compounded quarterly

ICICI - 11.2% p.a. compounded half yearly

HDFC- 11.5% p.a. compounded yearly.

In which bank should he deposit his money?

Solution:

Bank	Nominal / stated / normal Rate of interest (r)	Period of compounding	No. of compounding period in a year (m)	Effective rate of interest r_e = (1+r/m)^m -1
SBI	0.1075	Weekly	52	(1 + )⁵² -1 = 0.1134
PNB	0.11	Monthly	12	(1 + )¹² -1 = 0.1157
HSBC	0.1125	Quarterly	4	(1 + )⁴ -1 = 0.1173
ICICI	0.112	Half yearly	2	(1 + )² -1 = 0.1151
HDFC	0.115	yearly	1	(1 + )¹ -1 = 0.115
Ravi should invest in HSBC as effective rate of interest is highest for HSBC = 0.1173 or 11.73 %