What lump sum deposited today at 8 ?% compounded quarterly for 15 years will yield the same final amount as deposits of ?$6000 at the end of each? 6-month period for 15 years at 8 ?% compounded? semiannually?
The value of the lump sum is?
| $ 1,02,562.17 |
Working:
| a. | Calculate future value of 6-month deposits | |||||||||||
| Future Value | = | 6-month deposits x future Value of 6-month deposits for 15 years | ||||||||||
| = | $ 6,000.00 | x | 56.08494 | |||||||||
| = | $ 3,36,509.63 | |||||||||||
| Working: | ||||||||||||
| Future Value of 6-month deposits for 15 years | = | (((1+i)^n)-1)/i | Where, | |||||||||
| = | (((1+0.04)^30)-1)/0.04 | i | 4% | |||||||||
| = | 56.08494 | n | 30 | |||||||||
| b. | Present Value of amount to be deposited | |||||||||||
| Present Value | = | F*(1+i)^-n | Where, | |||||||||
| = | 336509.63*(1+0.02)^-60 | i | 8%/4 | = | 0.02 | |||||||
| = | $ 1,02,562.17 | n | 15*4 | = | 60 | |||||||
| F | = | $ 3,36,509.63 | ||||||||||
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