1. Imagine that a bank offers an interest rate of 4%, which is compounded quarterly. How much money should I deposit today in that bank so that it will grow over time and will reach 40000 in 5 years?
2. a. Jordan is buying a house which is listed in an ad with a price of $250000. On the day when he buys the house, he makes a downpayment of $30000 and he signs a 20 year mortgage agreement with an interest rate of 3%.
i. What is the principal amount of the mortgage?
ii. How much will he pay every month on a regular basis?
iii. How much total will he pay over the entire period (20 years) of the mortgage?
Solution 1:
Let amount to be deposited today = P
Future value = $40,000
Period = 5 years, 20 quarterly periods
Interest rate = 4%, 1% per quarter
P * (1+0.01)^20 = $40,000
P = $40,000 / 1.22019 = $32,782
Solution 2 (i):
Price of house = $250,000
Down payment = $30,000
Principal amount of mortgage = $250,000 - $30,000 = $220,000
Solution 2 (ii):
Interest rate = 3% p.a.,0.25% per month
Period = 20 years, 240 monthly periods
Monthly payment = $220,000 / Cumulative PV Factor at 0.25% for 240 periods
= $220,000 / 180.3109 = $1,220
Solution 2 (iii):
Total amount to be paid over the entire period of mortgage = $1,220 * 240 = $292,800
1. Imagine that a bank offers an interest rate of 4%, which is compounded quarterly. How...