Financial management
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Course
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University
Date
Your grandfather upon your birth invested $1000 into an account for you. The account has earned an annual rate of 12.27% a year. On your 21st birthday, you could withdraw the accumulated amount. How much can you withdraw?
S = P (1+r) n Let this be equation (i). Where S is the accumulated amount, P is the deposit (investment) r is the annual rate and n the number of years
P = $1000, r = 12.27% and n = 20
Therefore, S = 1000 (1 + 0.1227) 20
Calculating, S = $10122.18. This is the accumulated amount that can be withdrawn.
Now suppose, there is $29042 in the account. What rate of return did we receive?
Rate of return = (29042-10122.18)/29042
= (18919.81/29042) × 100
Rate of return = 65.15%
I want to have $30000 on my first birthday. If I could have earned 12.27% a year, how much would my grandfather have had to invest in the account for me to reach $30000?
Here, we are given S ($30000) and r (12.27). To find P, we substitute in equation (i)
Thus, 30000 = P (1 + 0.1227) 20
Making P the subject of the formula and solving for the value of P,
We get P = $2963.79
I want to take my family on vacation to Disneyland in three years. I believe I will need $20000 for the three weeks I plan to spend in Florida. I can earn 6%APR in my savings account for the bank. How much will I need to deposit each month to reach my goal?
S = R [(i+1)n -1)] /i
Where S = $20000, n = 3 years and i= 6%
R is the amount to be deposited each month.
Substituting for known values, 20000 = R [(0.06 + 1)3 -1)]/0.06
Making R the subject and solving for the value of R we get
R = $6282.19 per year
Thus, deposit per month = $ 6282.19/12
= $523.52
If I deposit $750 each month, how much will I have for my vacation?
Here, R = $ 750
Therefore, deposit per year = $750 × 12 = $9000
Putting the values in the above equation,
S = 9000 [(0.06 + 1)3 – 1]/0.06
S = $28652.4. This is the amount for the vacation.
If I made the first deposit today, how much will I have for my vacation?
S = P (1 + r)n
Deposit made today $9000, rate, r = 0.06, n = 3years
Therefore, S = 9000 (1 + 0.06)3
Solving for S, S = $10719.14. This is the amount that will be available for the vacation
I just won the lottery. I won $16000000 to be paid out over the next 20 years in equal payments. If the appropriate discount rate is 8%, how much in present value did I win?
P =[R {(i+1) n-1}]/ [i (1+i)]
R is the equal payments made yearly
P=$16000000
$1600000=[R {(0.08+1)20-1}]/ [0.08(1+0.08)]
Making R the subject and solving
R=$349635.34
P= [349635.35{(0.08+1)20-1}]/ [0.08(1+0.08)]
P=$3432771.31
How much did I win if the first payment is received today?
Yearly payments, R = $349635.34
Therefore, P = 349635.34(1 + 0.08)20
P = $1629635.34. This is the amount that I won
My friend has a business opportunity available to him. He says that if I invest with him I will receive $1250 a month for 4 years from the investment. I believe that for such a risky investment I need to get at least 20% return. How much is the most I should be willing to give him?
S is the sum total of amount received in the 4 years.
S=1250*12*4=$60000
$60000 is the total profit received on the investment
ROR=20%
(60000/P)*100%=20%
Solving for P we get, P=$300000
Give him $300000
If the investment is expected to last forever, how much is the most I should give him?
P = (15000)/ [(1 +0.02)4 -1)
Amount that should be given = $181967.8
I evaluate starting a business. I believe that I will make $12000 in year 1, $10000 in year 2, $7500 in year 3 and $4000 in year 4. I believe for a risky project like this, I should get at least a 16% return. What is the most I should be willing to invest?
Total amount made = (12000 + 10000 + 7500 + 4000) =$33500
Let the amount to be invested to be P
Therefore, rate of return = (33500/P) × 100 = 16%
Making P the subject and solving for value of P,
We get amount to be invested to be $209375
If I had only invested $20000, what rate of return would I receive?
Here, the value of P is $20000
Therefore, r = (33500/20000) × 100
Rate of return = 167.5%
I want to buy a car. The MSRP is $31000. I pay $516 per month for five years. The quoted APR is 6.9%. How much did I pay for the car?
S=R [(i+1) n-1]/i
n=5years, i=0.069
R is the equal yearly payments=$516*12=$6192
S= [6192{(1+0.069)5-1}]/0.069
S=$35537.59
If the best offer was $545 per month from the dealership, how much did they want for the car?
S=R [(i+1)n-1]/i
R=$(545*12) =$6540
S=6540[(0.069+1)5-1]/0.069
What is the balance, on the loan after 2.5 years, if I made every $516 payment on time?
S=R [(1+i) n-1]/i
R=$516*12=$6192
n=2.5years, i=0.069
S=6192[(1+0.o69)2.5-1]/0.069
S=$16290.22
How much of payment 2 is interest? How much goes to principal?
Principal
S=P (1+i) n
S=$37534.86
i=0.069,n=5years
Therefore 37534.86=P (1+i) 5
Solving P=$26887.24
Interest
Interest=p*i*n
i=26887.24*0.069*5=9276.09
i=$9276.09
If I make payments of $550 per month, how long will it take me to pay off the loan?
S=R [(1+i) n-1]/i
R= (550*12) =$6600
i=0.069
s=$35537.59
Substituting and solving for n we find
n=4.73 years
If the quoted APR on my credit card is 21.9%, what is the effective annual rate I am paying if the compounding period is monthly? Daily?
1+ieff= (1+r/m) m
m is the number of interest periods per year
r is the nominal interest rate (per year)
1+ieff= (1+0.219/12)12
- Monthly compounding
- m=12
ieff=1.2424-1=0.2424
ieff=24.24%
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