Question

1. A car’s price is currently $20,000 and is expected to rise by 6% a year. If the interest rate is 9%, how much do you need to put aside today to buy the car one year from now? Show your calculations!

1. 19,449.54
2. B. 18,348.62
3. C. 20,566.04
4. D. 18,867.93

2. What is the annually compounded rate of interest (EAR) on an account with an APR of 10% and monthly compounding? Show your calculations!

1. 10.00%
2. B. 10.47%
3. C. 10.52%
4. D. 11.05%

3. What is the present value of your trust fund if you have projected that it will provide you with $50,000 7 years from today and it earns 10% compounded annually? Show your calculations!

1. $29,411.76
2. B. $28,223.70
3. C. $25,657.91
4. D. $25,000.00

4. An investment of $100 pays interest of 2.5% per year. What will be the value of this investment at the end of 12 years? Show your calculations!
   1. $107.69
   2. B. $133.10
   3. C. $313.84
   4. D. $134.49

Answer 1

1) A) 19449.54

Here Inflation rate is 6% and nominal rate = 9%
Thus real rate = (1+nominal rate)/(1+inflation rate) - 1
= (1+9%)/(1+6%) - 1
=(1+0.09)/(1+0.06) - 1
= 1.09/1.06 - 1
=1.02830 - 1
= 2.83%

Thus FV = PV(1+r)^n
= FV = 20,000$
r = 2.83%
n = 1
Thus 20,000 = PV(1+2.83%)^1
=20,000 = PV(1.0283)
PV = 20000/1.0283
= $ 19449.54

2) B) 10.47%

EAR = (1+APR/n)^n - 1

n = no. of times of compounding

APR = 10%

EAR = (1+10%/12)^12 - 1

= (1+0.83333%)^12 - 1

=(1+0.0083333)^12 - 1

= 1.0083333^12 - 1

=1.1047 - 1

=0.1047

i.e 10.47%

3) C. $25,657.91

PV = FV/(1+r)^n
n = no. of years = 7
r = 10%
FV = 50,000 $
PV = 50,000/(1+10%)^7
= 50000/(1+0.1)^7
= 50000/(1.1)^7
= 50000/1.9487
= 25657.91 $

4) D. $134.49

FV = PV(1+r)^n
n = no. of years = 12
r = rate of interest = 2.5%
PV = 100$
PV =100(1+2.5%)^12
= 100(1+0.025)^12
= 100(1.025)^12
= 100(1.34488)
= 134.49 $