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Suppose you have a new baby and want to start saving for college. The average tuition, fees, and room and board charges at a local four-year institution totaled $26734 the year the child was born. Assuming a 2.3% annual increase to school costs, this cost will rise to $40255.51 when your child begins college in 18 years.How much do you need to invest now in an investment earning 4% compounded daily to be able to pay for your child's schooling?You will need to invest $

Question

Suppose you have a new baby and want to start saving for college. The average tuition, fees, and room and board charges at a local four-year institution totaled 26734theyearthechildwasborn.Assuminga2.326734 the year the child was born. Assuming a 2.3% annual increase to school costs, this cost will rise to 40255.51 when your child begins college in 18 years.How much do you need to invest now in an investment earning 4% compounded daily to be able to pay for your child's schooling?You will need to invest $

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Solution

To calculate the amount you need to invest now, you need to use the formula for the future value of a lump sum compounded daily. The formula is:

FV = PV * (1 + r/n)^(nt)

Where: FV = Future Value PV = Present Value r = annual interest rate (in decimal form) n = number of times interest is compounded per year t = number of years

In this case, you want to solve for PV because you want to know how much to invest now. So, rearrange the formula to solve for PV:

PV = FV / (1 + r/n)^(nt)

You know that FV = $40255.51 (the cost of college in 18 years), r = 0.04 (4% annual interest rate), n = 365 (interest is compounded daily), and t = 18 (18 years until college).

So, plug in these values to get:

PV = $40255.51 / (1 + 0.04/365)^(365*18)

Calculate the expression in the parentheses first:

1 + 0.04/365 = 1.000109589

Raise this to the power of 365*18:

(1.000109589)^(365*18) = 2.0255

Then divide the future value by this number:

40255.51/2.0255=40255.51 / 2.0255 = 19877.77

So, you need to invest approximately $19877.77 now to be able to pay for your child's schooling in 18 years.

This problem has been solved

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