Question 1187744: Sam Long anticipates he will need approximately $226,800 in 15 years to cover his 3-year-old daughter’s college bills for a 4-year degree.
How much would he have to invest today at an interest rate of 8% compounded semiannually? (Use the Table provided.) (Do not round intermediate calculations. Round your answer to the nearest cent.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i don't have a table, but i do have a formula and a calculator that can handle this.
he will need 226,800 in 15 years.
he will invest today at 8% per year compounded semi-annually.
the formula to use is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
the time periods are semi-annual.
you multiply the number of years by 2 to get the number of semi-annual periods.
you divide the interest rate per year by 2 to get the interest rate per semi-annual period.
the future value is 226,800.
you want to find the present value
the formula becomes 226,800 = p * (1 + .08/2) ^ (15 * 2)
simplify to get:
226,800 = p * 3.24339751.
solve for p to get:
p = 226,800 / 3.24339751 = 69,926.6739.
confirm by replacing p in the original equation and solving for f to get:
f = 69,926.6739 * 3.24339751 = 226,800.
if you have a table, it is probably a factor.
for 15 years compounded semi-annually, you are talking about 30 semi-annual periods with a future value factor of 1.04^30 = 3.24339751 which you round to whatever the table is saying.
for the same 15 years compounded semi-annually, you are talking about 30 semi-annual periods with a present value factor of 1/1.04^30 = .308318668 which you round to whatever the table is saying.
for example, a future value of 226,800 would be multiplied by .308318668 to get a present value of 69,926.6739 and a present value of 69,926.6739 would be multiplied by 3.24339751 to get a future value of 226,800.
not seeing your table, i don't know what it's in there and can only make an assumption.
if you can send me a copy of the table, i would probably be able to figure out how you would use it.
note that, to find the effective annual interest rate, you would take 1.04 ^ 2 = 1.0816/
that's your effective annual growth rate.
1. 0816^15 = 3.24339751.
this is the same growth factor as 1.04^30.
this makes sense because 1.04^30 = (1.04^2)^15.
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