Question

Complete the following problems in a word document. Please show values for all variables and circle the correct answer. Failure to do so will result in lost points.

You borrow $15,000 for your tuition costs. You agree to make payments at the end of each month for the next 10 years. If the interest rate on this loan is 6%, how much is your monthly payment? How much do you still owe after 20 payments?

Jill would like to plan for her son’s college education. She would like for her son, who was born today, to attend college for 5 years, beginning at age 18. Tuition is currently $12,000 per year and tuition inflation is 6%. Jill can earn an after-tax rate of return of 8%. How much must Jill save at the end of each year, if she wants to make the last payment at the beginning of her son’s first year of college?

Elin wants to retire in 20 years when she turns 60. Elin wants to have enough money to replace 120% of her current income less what she expects to receive from Social Security. She expects to receive $20,000 per year from Social Security in today’s dollars. Elin is conservative and wants to assume a 6% annual investment rate of return and assumes that inflation will be 3% per year. Based on her family history, Elin expects that she will live to be 95 years old. If Elin currently earns $100,000 per year and expects her raises to equal the inflation rate, approximately how much does she need at retirement to fulfill her retirement goals?How much does she need to save each year to fund the goal?

Answer 1

A) Principal amount, P = 15,000
interest rate per year = 6%
Interest rate per month, r = 6/12 = 0.5%
Total number of period = Total years * 12 = 10*12 = 120
So, Monthly payment, M = P*r*(1+r)^n / ((1+r)^n - 1)
Putting the value in the formula,
M= 165.34
Total payments= M * Total period = 165.34 * 120 = 19,840.32
After 20 payments you will owe = Total - 20*M = 19,840.32 - 20*165.34 = 16,533.52

B) We have to use financial calculator here;
Given: Tution fees = 12000
Tution Inflation = 6%
After tax returns = 8%
Now,
PV = 12000; N = 18 years; I = 6%; PMT = 0
Using financial calculator,
The value of tutuion fees at the time of joining = 34,252.07 (FV)
Now, to calculate for 5 year
PMT = previous FV = 34,252.07
No. of years, N = 5;
Interest, I = ((1.08/1.06)-1)*100= 1.88 % (8% to compensate for after tax returns)
Now, PV for annuity = 162,009.57 (Using financial calculator)

Now to find out yearly savings needed,
FV = 162,009.57
N= 18 years
I = 8% (After tax returns)
Hence, PMT = 4,326 (Using financial calculator)

C) Given:

Years left for retirements, N = 20
Growth rate of salary, g = 3% (equal to inflation rate)
Inflation rate, r = 3%
Interest rate, I = 6%
Current salary, S = 100,000
Replacement percentage of salary, P = 1.2
Retirement duration, D = 95-60 = 35
Social security support, M = 20,000

Now, First withdrawal at the age of 65, W = ((1+g)^N)*((S*P)-M)
W = 180,611

Retirement fund required = (((W*(1+r))/(I-r))*(1-((1+r)/(1+I))^(D-1))) + W
= 4,045,303