Sam Long anticipates he will need approximately $225,000 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?

The amount of funds to be invested today is  $69,371.70  

Explanation:

The amount to be invested today can be computed using the modified present value formula as shown below:

Present value=fv*(1+r/2)^-(N*2)

The number 2 is to show that interest is semi -annual

fv is the amount of funds expected in 15 years of $225,000

r is the rate of return at 8% annually

N is the number of years of savings which is 15

pv=225000*(1+8%/2)^-(15*2)

   =225000*(1.04)^-30

   =225000*0.308318668

pv=$69,371.70  

$69371.1

Explanation:

To calculate how much Sam long anticipate to need approximately use the following method

We are given the following values

A = 225000

rate (r) = 8/100 = 0.08%

n = 2

t = 15years

Using the following formula

A = P ( 1 + r/n) ^ nt

Substituting it in to the formula, we have

225000 = P ( 1 + (0.08/2)^30

Making P the subject of formula

P = 225000 / ( 1 + (0.08/2)^30

Because P is what we need to find, which is the principal

P = 225000 / ( 1 + (0.08/2)^30

P = $69371.1

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