Find the future values of the following ordinary annuities: FV of $600 paid each 6 months for 5 years at a nominal rate of 13% compounded semiannually. Round your answer to the nearest cent. $ FV of $300 paid each 3 months for 5 years at a nominal rate of 13% compounded quarterly. Round your answer to the nearest cent. $ These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?
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| answer a) | Future value = | |||||||||
| we have to use fiancial calculator to solve this problem | ||||||||||
| Put in calculator | ||||||||||
| PV | 0 | |||||||||
| PMT | -600 | |||||||||
| I =13%/2 | 6.50% | |||||||||
| N=5*2 | 10 | |||||||||
| Compute FV | $8,096.65 | |||||||||
| answer b) | ||||||||||
| we have to use fiancial calculator to solve this problem | ||||||||||
| Put in calculator | ||||||||||
| PV | 0 | |||||||||
| PMT | -300 | |||||||||
| I =13%/4 | 3.25% | |||||||||
| N=5*4 | 20 | |||||||||
| Compute FV | $8,269.27 | |||||||||
| answer c) | ||||||||||
| Annuity in 2nd part is compounded more frequently, therefore, more interest is earned on previously earned interest | ||||||||||
| Hence, FV of 2nd option is higher even contributed amount is same and APR (interest rate) is also same. | ||||||||||
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