Suppose that your child is born this year, and that you would like to set aside enough money now so that your child will have $3000000 at retirement in 20 years.
A) if return of return on your money averages 5% per year over the next 70 years, how much do you have to invest today so that your child will have $3000000 in 70 years
B) suppose that your child decides to retire at the age of 50 instead, how much money will there be based on the assumption and answers from part A above?
A*1.05^70 = 3000000
now take logs and solve for logA
or, A = 3000000/1.05^70
= (3000000^(1/70)/1.05)^70
To calculate the amount of money you need to invest today so that your child will have $3,000,000 at retirement in 20 years, we can use the concept of compound interest.
A) Assuming a return on investment of 5% per year over the next 70 years, we need to calculate the present value of $3,000,000 at the end of 70 years.
The formula to calculate the present value (PV) of a future amount is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest Rate
n = Number of years
In this case, FV is $3,000,000, r is 5% (or 0.05), and n is 70.
Using these values, we can substitute them into the formula:
PV = 3,000,000 / (1 + 0.05)^70
Now let's solve for PV:
PV = 3,000,000 / (1.05)^70
PV = 3,000,000 / 21.724811
Rounding the answer to the nearest dollar, the amount you need to invest today is approximately $138,136.
B) If your child decides to retire at the age of 50 instead, we can use the same amount calculated in part A, and let it grow for an additional 20 years until retirement.
To calculate the future value (FV) based on the assumption and answer from part A, we can use the formula:
FV = PV * (1 + r)^n
Where:
FV = Future Value
PV = Present Value
r = Interest Rate
n = Number of years
Using the value calculated in part A as PV ($138,136), and assuming a return on investment of 5% per year, we need to calculate the future value after an additional 20 years (n = 20):
FV = 138,136 * (1 + 0.05)^20
Now let's solve for FV:
FV = 138,136 * (1.05)^20
Rounding the answer to the nearest dollar, the amount of money at retirement based on the assumption and answers from part A will be approximately $780,156.