Nathan and Stephanie are saving for their daughter's college education. Their daughter, Paige, is now 8 years old and will be entering college 10 years from now (t = 10). College tuition and expenses at State U. are currently $16,000 a year and are expected to increase at a rate of 4% a year. They expect Paige to graduate in 4 years (if Paige wants to go to graduate school, she's on her own). Tuition and other costs will be due at the beginning of each school year (at t = 10, 11, 12, and 13). So far, Nathan and Stephanie have built up $9,000 in the college savings account. Their long-run financial plan is to contribute $3,000 a year at the beginning of each of the next five years (at t = 0, 1, 2, 3, and 4). Then they plan to make 6 equal annual contributions at the end of each of the following 6 years (t = 5, 6, 7, 8, 9, and 10). Their investment account is expected to earn 8%. How large must the annual payments be in the subsequent 6 years (t = 5, 6, 7, 8, 9, and 10) to meet their daughter’s anticipated college costs?Can you explain about the formula used here? Computation of Future worth of AnnualContribution and Savings at the end of year4:Euture worth of Annual Cont on in Yeae 4 =>Payment x Cz+ JesS-1=>3eo x (1+o08)-13000% 5.8664$17 599.8029Euture lalue of CwrentSavings-s CurrentSening C1+ cS=) $12244.4006Tatal Euture Velue of Contri bution andSavinge$(14599. 8029 + 12244.4006) -| $ 2984 4. 2035in Year 4:- To Compute Annual Payments first werequired to calculate the present worth ofcollege tuition fees in 10th year byconsidering inflation:Present - Darth - Tution fees (1 +)+(itoo4)1216రార=> 1boco (1 tor04)"(ito o8)°16oro +Cito04)".16cro + Cito.o4ys)=) $( 23,683.9085 + 22806 4268+ 21962 0 331 + 21 148.6245=) $ 89601· 24 3CS Scanned with CamScanner

In the given question first calculated future worth of present saving and future worth of the…

Answered: Nathan and Stephanie are saving for…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Nathan and Stephanie are saving for their daughter's college education. Their daughter, Paige, is now 8 years old and will be entering college 10 years from now (t = 10). College tuition and expenses at State U. are currently $16,000 a year and are expected to increase at a rate of 4% a year. They expect Paige to graduate in 4 years (if Paige wants to go to graduate school, she's on her own). Tuition and other costs will be due at the beginning of each school year (at t = 10, 11, 12, and 13). So far, Nathan and Stephanie have built up $9,000 in the college savings account. Their long-run financial plan is to contribute $3,000 a year at the beginning of each of the next five years (at t = 0, 1, 2, 3, and 4). Then they plan to make 6 equal annual contributions at the end of each of the following 6 years (t = 5, 6, 7, 8, 9, and 10). Their investment account is expected to earn 8%. How large must the annual payments be in the subsequent 6 years (t = 5, 6, 7, 8, 9, and 10) to meet their daughter’s anticipated college costs?

Can you explain about the formula used here?

Computation of Future worth of Annual
Contribution and Savings at the end of year
4:
Euture worth of Annual Cont on in Yeae 4 =>
Payment x Cz+ JesS-1
=>
3eo x (1+o08)-1
3000% 5.8664
$17 599.8029
Euture lalue of Cwrent
Savings-s Current
Sening C1+ cS
=) $12244.4006
Tatal Euture Velue of Contri bution and
Savinge
$(14599. 8029 + 12244.4006) -| $ 2984 4. 2035
in Year 4:-

To Compute Annual Payments first we
required to calculate the present worth of
college tuition fees in 10th year by
considering inflation:
Present - Darth - Tution fees (1 +)
+(itoo4)
12
16రార
=> 1boco (1 tor04)"
(ito o8)°
16oro +Cito04)".
16cro + Cito.o4ys
)
=) $( 23,683.9085 + 22806 4268
+ 21962 0 331 + 21 148.6245
=) $ 89601· 24 3
CS Scanned with CamScanner

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