If a father wants to have $100,000 to send a newborn child to college, how much must he invest annually for 18 years if he earns 9 percent on his funds?
P(1.09)^18=100 000
P=100 000/4.72
paym(1.09^18 - 1).09 = 100 000
paym( 41.301338)
annual investment = 100 000/41.301338) = 2412.23
To determine the amount the father must invest annually, we can use the concept of compound interest.
Compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount (in this case, $100,000)
P = the principal amount (the amount the father needs to invest annually)
r = the annual interest rate (9% or 0.09)
n = the number of times interest is compounded per year (assuming it's compounded annually, so n = 1)
t = the number of years (18 in this case)
We can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Substituting the given values:
P = 100,000 / (1 + 0.09/1)^(1*18)
Now let's solve this equation step by step:
1. First, divide the interest rate by the number of compounding periods:
r/n = 0.09/1 = 0.09
2. Next, raise the result to the power of (nt):
(1 + 0.09)^18 = 2.3673
3. Divide the final amount by the result from step 2:
100,000 / 2.3673 ≈ 42,219.44
Therefore, the father must invest approximately $42,219.44 annually for 18 years at a 9% interest rate to accumulate $100,000 to send the newborn child to college.