Your company has money to invest in an employee benefit plan and you have been chosen to be the plan's trustee. As an employee you want to maximize the interest earned on this investment and have found an account that pays 10% compounded continuously. Your company is providing you with $ 1,500 per month to put into your account for 10 years. What will be the balance in this account at the end of the 10-year period

The balance in this account at the end of the 10-year period is 310000

Explanation:

Solution

Given that:

Now, Recall that,

Time period is = 10 yrs = 12*10 = 120 months

Interest = 10%

= 10%/12 = 0.8333% per month continuously compounded.

Thus,

The rate effective per month = e^r - 1 = e^0.0083333 - 1 = 0.00836815

so,

The month per = 1500

The value of future deposit = 1500 * (F/A, 0.836815%,120)

= 1500 * [ ((1 + 0.00836815) ^120 - 1) / 0.00836815]

= 1500 * [ ((1.00836815) ^120 - 1) / 0.00836815]

= 1500 * 205.3359

= 308003.89

which is also = 310000 (nearest value)