Question

Brenda Young desires to have $20,000 eight years from now for her daughter's college fund. If she will earn 4% (annually compounding) on her money, approximately what amount should she deposit now?

Answer 1

Answer: $14613.80

Explanation: we use the equation $P= C(1 +i)^n$

where P is the future value of an investent in this case its $20000.

C is the present invested value which we are going to calculate.

I is the interest rate at a given period in this case 4%

n is the period of the investment which is 8 years in this case

so then now we substitute the values we have to the above formula

$20000= C(1+ 0.04)^8$

thereafter we rearrange the formula and solve for c the present initial invested value: $20000/(1.04)^8 = C$

then we get an answer of $14613.8041 which we round off to $14613.80.

the key points to this problem is that brenda desires $20000 for her daughters college fund which tells us that she wants to invest a certain amount of money to have a future value of $20000 for her daughter. we also are given another key that that certain unknown amount of money she will annully compound for 8 years which gives the period. thereafter the question leads us to what amound should brenda deposit now  that makes the question clear that we must calculate the initial investment she must make.

Answer 2

Answer:

The amount of deposit required now is $14,613.80 in order to have $20000 in the account in 8 years' time

Explanation:

By using present value formula as shown below we can determine amount to  be deposited now.

PV=FV/(1+r)^n

PV=present value=unknown

FV=Future value =$20000

r=rate of return=4%

n=number of years of investment=8 years

PV=20000/(1+0.04)^8

PV=20000/(1.04)^8

PV=20000/1.36856905

PV=$14613.80

The difference between the FV and PV is $5386.20 when divided by 8 years gives  about $637.27 as average yearly overall return on the deposited funds.