Question

Imagine that Homer Simpson actually invested ​$100 comma 000 5 years ago at a 7.5 percent annual interest rate. If he invested an additional ​$1 comma 500 a year at the beginning of each year for 20 years at the same 7.5 percent annual​ rate, how much money will Homer have 20 years from​ now

Answer 1

Answer:

Total amount of money on both investments in 20 years will be $679,663

Explanation:

Firstly, we calculate the the return in the next 20 years expected on $100,000 , invested 5 years ago.

The mathematical formula to use is :

Future value = Present Value * (1 + interest rate)^number of years

The twist here is that the number of years is 25 and not 20 or 5. This is because he had invested 5 years ago and he’s expecting a return in the next 20 years. So total investment time would be 5 + 20 = 25 years

Future value = 100,000 * (1 + 7.5/100)^25

= 100,000 * (1+0.075)^25

= 100,000* (1.075)^25

= $609,834

Secondly, we now calculate the future value for an additional $1,500 per year for 20 years at same interest percentage

We use a mathematical approach to this also.

The formula to use is:

Future value = Annual payment * {[1+r]^n -1}/r * [1+r]

Where r is interest rate = 7.5/100 = 0.075, n = number of years and Annual payment = $1,500

We substitute these values;

Future Value = $1,500 * {[1+0.075]^20 - 1}/0.075}* (1 + 0.075)

Future value = 1,500 * [1.075]^20 - 1]/0.075 * 1.075

Future Value = $69,829

Thirdly, the total amount of money he would have on both investments at the end of the years later.

Total amount of money = $609,834 + $69,829 = $679,663

Answer 2

Answer:

Step 1: Calculate the future value for $100,000 for 25 years at 7.5% interest rate as follows:

Here, the investment was made 5 years ago and the money HM will have 20 years from now will total add to 25 years.

$Future value = Present value * (1 + Interest rate)^{Years}$

Future Value = $100,000 * (1 +0.075)^{25}$

Future Value = $100,000 * (1.075)^{25}$

Future Value = $ 100,000 x 6.0983396

Future Value = $609,833.961

Step 2: Calculate the future value for additional $1,500 a year from today at the beginning of each year for 20 years at 7.5% annual interest rate as follows:

$Future value = Yearly payment * \frac{1 + Interest Rate^{Years} - 1 }{Interest Rate} * (1 +Interest Rate)$

$Future value = 1500 * \frac{1 + 0.075^{50} - 1 }{0.075} * (1 + 0.075)$

Future Value = $69,828 .80

Step 3: Calculate the total money HM will have at the end of 20 years as follows:

Total money = Future value of $100,000 +  Future value of yearly investment of $1,500

Total money = $609,833.96 + $69,828.80

Total money = $679,662.76  

   

Therefore. the total money HM will have at the end of 20 years is $679,662.761