Respuesta :
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.
[tex]Future value = Present value * (1 + Interest rate)^{Years}[/tex]
Future Value = [tex]$100,000 * (1 +0.075)^{25}[/tex]
Future Value = [tex]$100,000 * (1.075)^{25}[/tex]
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:
[tex]Future value = Yearly payment * \frac{1 + Interest Rate^{Years} - 1 }{Interest Rate} * (1 +Interest Rate)[/tex]
[tex]Future value = 1500 * \frac{1 + 0.075^{50} - 1 }{0.075} * (1 + 0.075)[/tex]
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
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
