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SE261
HW4
02-17-2022
Siddh Saraogi
Section G
Effective Annual Interest Rate, I =(1+r/m)^m−1
where:
r=Nominal interest rate
m=Number of periods
Effective rate
Nomina
l rate
Compoundin
g annually
Compoundin
g semi-
annually
Compoundin
g quaterly
Compoundin
g monthly
Compoundin
g daiy
Continuous Compoundin
g
6%
6%
6.09%
6.13%
6.16%
6.18%
6.18%
8.4%
8.4%
8.58%
8.66%
8.73%
8.76%
4.21%
4.21%
4.25%
4.27%
4.3%
6.97%
7.2%
7.22%
7.22%
Problem #2 a) You have $35,000 and want to buy a house. After a search you find your dream house but the owner is asking for $80,000. The owner will not bargain but he is willing to wait for you to get the money together. Your only choice is to put the money in the bank with a 10% interest rate. How many years do you have to wait to buy your dream house if the interest is compounded –
1) Quarterly 2) Monthly 3) Continuously b) If the seller says that he will only wait a maximum of 4 years, how much money do you need to put in your bank account today for the same 10% interest rate when compounded –
1) Quarterly 2) Monthly 3) Continuously to purchase the house in 4 years?
Using the formula A=P(1+r/4)^4m
where
A=future value
P=present value
r=rate of interest
t=time period.
80,000=35000*(1+0.1/4)^4t
(80,000/35000)=(1+0.025)^4t
2.28571429=(1.025)^4t
Taking log on both sides;
log 2.28571429=4t*log (1.025)
0.359021943=4t*0.0107238654
t=1/4*(0.359021943/0.0107238654)
=8.37 years
b. Using the formula A=P(1+r/12)^12n
where
A=future value
P=present value
r=rate of interest
t=time period.
80,000=35000*(1+0.1/12)^12t
(80,000/35000)=(1+0.00833333333)^12t
2.28571429=(1.00833333333)^12t
Taking log on both sides;
log 2.28571429=12t*log (1.00833333333)
0.359021943=12t*0.00360412427
t=1/12*(0.359021943/0.00360412427)
=8.30 years
c.We use the formula:
A=P(e)^rt
where
A=future value
P=present value
r=rate of interest
t=time period.
e=2.71828
80,000=35000*(2.71828)^(0.1t)
(80,000/35000)=(2.71828)^(0.1t)
2.28571429=(2.71828)^(0.1t)
Taking log on both sides;
log 2.28571429=(0.1t)*log (2.71828)
0.359021943=(0.1t)*0.43429419
t=1/0.1*(0.359021943/0.43429419)
=8.27 years
2.a.Using the formula A=P(1+r/4)^4t
where
A=future value
P=present value
r=rate of interest
t=time period.
80,000=P*(1+0.1/4)^(4*4)
80,000=P*(1+0.025)^(16)
80,000=P*(1.025)^(16)
P=80,000/(1.025)^(16)
=80,000*0.673624934
=$53889.99
b.Using the formula:
A=P(1+r/12)^12t
where
A=future value
P=present value
r=rate of interest
t=time period.
80,000=P*(1+0.1/12)^(12*4)
80,000=P*(1+0.00833333333)^(48)
80,000=P*(1.00833333333)^(48)
P=80,000/(1.00833333333)^(48)
=80,000*0.671431999
=$53714.56
c.We use the formula A=P(e)^rt
where
A=future value
P=present value
r=rate of interest
t=time period.
e=2.71828
80,000=P*(2.71828)^(0.1*4)
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