1.TimeValue 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. Calculatehow much he will receive after the end of 1st, 2nd and 3rd year of hisinvestment?
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 × FVFr, n = 710000 × PVF.1,1 = 710000 × 1.1 = 781000
A | B | A × B |
Present value at year 0 | FVFr,n ( r= 0.1, n=1,2,3) taken from PVF table | Future Value at the end of |
Rs. 7,10,000 | FVF0.1, 1 = 1.1 | Year 1 - FV1 = PV × FVF0.1, 1 = Rs. 7,10,000 × 1.1 = Rs. 7,81,000 |
Rs. 7,10,000 | FVF0.1, 2 = 1.21 | Year 2 - FV2 = PV × FVF0.1, 2 = Rs. 7,10,000 × 1.21 = Rs. 8,59,100 |
Rs. 7,10,000 | FVF0.1, 3 = 1.33 | Year 3 - FV3 = PV × FVF0.1, 3 = Rs. 7,10,000 × 1.33 = Rs. 9,65,600 |
2. Mr. X invested Rs. 1,000, Rs. 2,000and 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 therate 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 valueof 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 3years at an interest rate of 12 % per annum compounded semiannually. Whatamount he will get after 3 years?
Solution:
FV = PV ×FVF 0.06, 6 = Rs. 7,000 × 1.419 = Rs. 9,933
(In case ofsemiannual compounding divide r by 2 and multiply n by 2)
5. Vitthal has invested Rs. 25, 000now for 3 years at the rate of 8 % per annum compounded quarterly. What amounthe 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 multiplyn by 4)
6.Ravi wants to deposit Rs. 10, 00,000 in a bank for a year. He has receivedfollowing 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.
Inwhich 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 re = (1+r/m)m -1 |
SBI | 0.1075 | Weekly | 52 | (1 + |
PNB | 0.11 | Monthly | 12 | (1 + |
HSBC | 0.1125 | Quarterly | 4 | (1 + |
ICICI | 0.112 | Half yearly | 2 | (1 + |
HDFC | 0.115 | yearly | 1 | (1 + |
Ravi should invest in HSBC as effective rate of interest is highest for HSBC = 0.1173 or 11.73 % |
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