Answer:
The answer is $343,934.91 (to the nearest cent.)
Explanation:
For the second option, we will calculate the future value of an amount invested for a period of time, which is compounded periodically, using the formula:
![FV=PV(1+\frac{r}{n} )^{n*t}](https://tex.z-dn.net/?f=FV%3DPV%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bn%2At%7D)
where:
FV = future value = ?????
PV = present value = $10,000
r = interest rate in decimal = 9.6% = 9.6/100 = 0.096
n = frequency of compounding in a year = monthly = 12
t = time = 18 years to 55 years = 55 - 18 = 37 years, \
Therefore:
![10,000(1+\frac{0.096}{12} )^{(12*37)}\\= 10,000*(1.008)^{444} \\= 10,000 * 34.39349075 = 343,934.908](https://tex.z-dn.net/?f=10%2C000%281%2B%5Cfrac%7B0.096%7D%7B12%7D%20%29%5E%7B%2812%2A37%29%7D%5C%5C%3D%2010%2C000%2A%281.008%29%5E%7B444%7D%20%5C%5C%3D%2010%2C000%20%2A%2034.39349075%20%3D%20343%2C934.908)
∴ FV = $343,934.91 (to the nearest cent.)
<em>Note that rounding off to the nearest cent means rouding off to the nearest hundredth or to two decimal places.</em>
Therefore under the second plan, at age 55, he will be given $343,934.91.
Also, if we are asked to compare both options to choose which is better,
for option 1 which will pay him $15,000 for each year of service (that is from 18 years to 55 years):
Years of service = 37 years
lump sum per year = $15,000
Therefore total amount from option 1 = 15,000 × 37 = $555,000
Therefore, at age 55, option 1 is better than option 2.
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