Problem 1

a. What do you expect tuition and housing at top private schools to cost during Mary’s first year at college?

PV=35,000; r=4%; N=18-5=13

FV=PV*(1+r)n =35,000*1+4%13 =58277.57

b. In nominal dollars, how much must be in the savings account on Mary’s 18th birthday after the last deposit has been made but before the first tuition and housing payment?

PV18=58277.57; g=4%; r=10%*(1-τ)=10%*（1-30%）=7%; N=3
Pmt19=PV18*1+g=58277.57*1+4%=60608.67

The present value of year 18-21 at 18th year is:
PV18-21=PV18+Pmt19r-g(1-(1+g1+r)N)
=58277.57+60608.677%-4%1-1+4%1+7%3 =223488.53

c. What should be the amount of the first deposit to the savings account?

FV=223488.53; r=10%*(1-τ)=10%*（1-30%）=7%; g=2%; N=18-5=13

Pmt1=FV1+rN-1+gNr-g =223488.531+7%13-1+2%137%-2% =10010.79

d. Alternatively, Mary’s parents could open a 529 account that allows college savings to grow tax-free. If they saved in this account rather than in a normal investment fund, and still earned the same pre-tax return, how much should be their first deposit?

PV18=58277.57; g=4%; r=10%; N=3;
Pmt19=PV18*1+g=58277.57*1+4%=60608.67

The present value of year 18-21 at 18th year is:
PV18-21=PV18+Pmt19r-g(1-(1+g1+r)N)
=58277.57+60608.6710%-4%1-1+4%1+10%3 =214721.71

FV=214721.71; r=10%; g=2%; N=18-5=13

Pmt1=FV1+rN-1+gNr-g =214721.711+10%13-1+2%1310%-2% =7957.58

Problem 2

a. What would be their monthly payment?

PV=300000-60000=240000; r=6.5%/12=0.00542; N=30*12=360

Pmt=PV1r-1r1+rN =24000010.00542-10.005421+0.00542360 =1516.96

b. Suppose the couple takes the mortgage. After 5 years, what would be the remaining principal amount owed on the mortgage?

PV=240,000; r=6.5%/12=0.542%; N=5*12=60; Pmt=1516.96