In: Economics
Ruby Rose will be in graduate school for the next three years. She borrowed some money from the bank for her graduate education, which the bank has accepted to be paid after Ruby graduates from school in two years.
The bank has accepted to the following payment plan: from the beginning of Year 4 (37th month) to end of year 5 (60th month), pay $600 in month 37 and increase payment by 4% every month thereafter.
How much money should Ruby Rose put aside each month (equal amount) for the first 36 months (during graduate school) such that she can pay the loan back after graduation? The bank charges an APR of 18%, compounded monthly.
Question 4 Part C: Provide the Present Value of the gradient, and then determine the value Ruby must set aside.
i = 18% / 12 = 1.5% per month
t = 2*12 = 24 months
First payment = 600
g = 4%
Present worth of geometric series = A*[1-(1+g)^n/(1+i)^n]/(i-g)
Present worth of payments at EOY 3 = 600*[1-(1+0.04)^24/(1+0.015)^24]/(0.015-0.04)
= 600*[1-(1.04)^24/(1.015)^24]/(-0.025)
= 600*31.7257537
= 19035.45
Present worth of gradient at EOY 0 = 19035.45*(P/F,1.5%,36)
= 19035.45*0.585090
= 11137.45
Monthly deposit amount = 19035.45*(A/F,1.5%,36)
= 19035.45*0.015/((1 + 0.015)^36-1)
= 19035.45*0.015/((1.015)^36-1)
= 19035.45*0.021152
= 402.64