can anyone help me set up this problem bc im totally lost....
if a house = $125,000 you want to buy this house in 10 years its expected to increase 5% a year over a 10 year period assuming you can earn 10% annually on investment. how much should you invest at the end of each of the next 10 years to be able to buy that house?
A calculator with an exponential function (or an Excel spreadsheet) is very helpful for solving this kind of problem. In 10 years the house will cost 125000*(1.05)^10 =203612.
Solve for X where X*(1.10)^10 = 203612. I get 78501.
To solve this problem, we need to calculate how much you should invest at the end of each year for the next 10 years in order to buy the house.
Here's the step-by-step explanation:
Step 1: Calculate the expected future value of the house after 10 years.
To do this, we take the initial value of the house ($125,000) and calculate its compounded value after 10 years at an annual growth rate of 5%.
Future Value of the House = Initial Value * (1 + Growth Rate)^Number of Years
Future Value of the House = $125,000 * (1 + 0.05)^10
Future Value of the House = $125,000 * (1.05)^10
Future Value of the House ≈ $125,000 * 1.6289
Future Value of the House ≈ $203,612.50
So, the expected future value of the house after 10 years is approximately $203,612.50.
Step 2: Calculate the annuity payment required to reach the future value.
To do this, we need to find the annuity payment required to reach the future value of the house ($203,612.50) after 10 years, assuming an annual interest rate of 10%.
Annuity Payment = Future Value / (1 + Interest Rate)^Number of Years
Annuity Payment = $203,612.50 / (1 + 0.10)^10
Annuity Payment ≈ $203,612.50 / 2.5937
Annuity Payment ≈ $78,605.22
So, you would need to invest approximately $78,605.22 at the end of each year for the next 10 years to be able to buy the house in 10 years, considering the expected increase in house value and assuming a 10% annual return on investment.