To find out how much the second partner should contribute in 8 years to match the investment of $10,000 made by the first partner, we can use the concept of compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value (amount accumulated after time t)
P = the principal amount (initial investment)
r = annual interest rate (written as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, the first partner invests $10,000 immediately, so P = $10,000. The interest rate is 4% per year and compounded quarterly, so r = 0.04 and n = 4.
Let's calculate the future value of the $10,000 investment after 8 years:
A = $10,000(1 + 0.04/4)^(4*8)
A = $10,000(1 + 0.01)^32
A = $10,000(1.01)^32
Using a calculator or spreadsheet, we find that A ≈ $10,998.87. This is the future value of the first partner's investment in 8 years.
Now, we need to find out how much the second partner should contribute in 8 years to match this amount. Let's call this amount X.
X(1 + 0.04/4)^(4*8) = $10,998.87
X(1.01)^32 = $10,998.87
Dividing both sides by (1.01)^32, we get:
X = $10,998.87 / (1.01)^32
Using a calculator or spreadsheet, we find that X ≈ $8,664.62. Therefore, the second partner should contribute approximately $8,664.62 in 8 years to match the first partner's investment of $10,000 made now.