HW Week 1, due on Canvas at 630 pm Tuesday Sep 1
August 27, 2020
1. Citibank pays 1% per year on their savings accounts, but charges 4% per year on loans they make to you. Which interest rate will you use to take present or future values in the following situations? In each situation find the amount indicated. When you are moving a cashflow from where it is into its future, use the future value formula. FV =PV(1+r)T PV is the cashflow you start with, T is the number of years you are moving the cashflow, and r is the interest rate per year. When you are moving a cashflow from where it is into its past, use the present value formula. FV PV = (1+r)T
(a) My baby daughter has just been born, and I invest $20,000 today to pay for her college education. I need to find out how much I will have on her 17th birthday. Here I am asked to move a cashflow from today into the future, so I need the future value formula:
FV =PV(1+r)T
I know that PV = 20, 000, and I am allowing the cash to grow for seventeen years, so T = 17. It's clear that I am saving, so the interest rate that is relevant is the 1%. So we get
FV = PV(1 + r)T = 20,000(1 +.01)17 = 20,000(1.1843) = 23,686.09
(b) My credit card debt of $20,000 has an extortionate interest rate of 24% per year. If I don't do anything, how much will I owe three years from today? I know that PV = 20,000, and I am allowing the amount I owe to grow for three years, so T = 3. Since the amount grows at whatever rate the credit card company is charging (24%), r = 24%. Citibank's rates are irrelevant: the credit card company doesn't care what Citibank is offering. So
1
FV = PV(1 + r)T = 20,000(1 + .24)3 = 20,000(1.9066) = 38,132.48
(c) My credit card debt of $20,000 has an extortionate interest rate of 24% per year. I "refinance" the debt: I pay off the credit card completely by getting money from "somewhere". I need to calculate how much I will need to pay on the amount I got from "somewhere" in 3 years.
from somewhere. I only have Citibank to borrow that $20,000 from, and since I am borrowing, the amount I borrow will grow at Citibank's loan interest rate of 4%. I borrow the money today, and allow it to grow for 3 years, i.e., I am moving that cash into the future, I need to find the future value. So
FV = PV(1 + r)T = 20,000(1 + .04)3 = 20,000(1.1248) = 22,497.28
(d) I am planning to buy a fancy mattress two years from today. The mattress costs $4,000. I won't have any money of my own at the time I buy the mattress. How much will I owe five years from today?