Financial management

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Course

Lecturer

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 21****st**** 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 This is the accumulated amount that can be withdrawn.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+i****eff****= (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

**i****eff****=24.24%**

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