Question

You think that in 15 years, it will cost $226,000 to provide your child a 4-year college education. Will you have enough if you take $69,000 today and invest it for the next 15 years at 5 percent? Round the answer to the nearest cent. Round FV-factor and FVA-factors to three decimal places.

__________(Select Yes or No), you will have approximately $________ _______(Select More or Less) than your estimate of $226,000.

If you start from scratch, how much will you have to save each year to have $226,000 in 15 years if you can earn a 5 percent rate of return on your investments?

Calculate your answer based on the FVA-factor.

$ _______

Calculate your answer based on the financial calculator.

$ _______

Answer 1

1) Required Amount (Future value) = $226,000

years = 15

Investment today (Present Value) =$69,000

Interest = 5%

then what we get after investment of $69,000, for 15years at 5% interest rate

FV = PV (1+i)^n

FV = 69,000(1+0.05)^15

= 69,000 * 2.079

= 143,451

NO, Required Amount (Future value) = $226,000

Value after calculation =  143,451

difference is = 226,000 - 143,451 = 82,549

2)

Required Amount (Future value) = $226,000

years = 15

Interest = 5%

how much will you have to save each year (Annuity) = A

FV_A = A [ ((1+i)ⁿ - 1) /  i ]

Calculate your answer based on the FVA-factor.

226,000 = A * FVA-factor

226,000 = A * 21.5786     FVA-factor = 21.5786

A = 10,473.36

we have to save each year (Annuity) = 10,473.36  

Calculate your answer based on the financial calculator.

226,000 = A [ ((1+0.05)¹⁵ - 1) / 0.05 ]

226,000 = A * 21.579

A = 10,473.15

we have to save each year (Annuity) = 10,473.15

almost same whether we calculate with FVA factor or financial calculator, slight difference will be from roundoff decimals