a. If you wish to have $250,000 in a savings account at the end of 10 years and
ID: 2418086 • Letter: A
Question
a. If you wish to have $250,000 in a savings account at the end of 10 years and you expect the account to earn a nominal rate of 6% per year compounded monthly how much will you need to deposit per month? (Answer is $1525.)
b. If Miss Taylor finances $200,000 for a home at a nominal rate of 5.3% compounded monthly for 30 years, what will her monthly payment be? (Answer is $1,111.)
c. A company wishes to make an investment now that is expected to generate a profit of $20,000 next year and decrease by $500 each year thereafter for a total of 20 years. How much should the company be willing to invest if they prefer to earn 10% per year on their investments? (Answer is $142,568.)
d. Suppose I invest $10,000 today and would like to have $20,000 five years from now. What interest must I earn per year?
Explanation / Answer
a monthly interest = 0.50% Future value of annuity = A*[(1+k)^n-1]/k A= monthly deposit k= 0.50% n=120 months 250000=A*[1.005^120-1]/0.005 A= 1525 So monthly deposit required = 1,525.00 b Formula for loan amortization = A= [i*P*(1+i)^n]/[(1+i)^n-1] Loan amount= 200,000 Amt $ A = periodical installment ? per month P=Loan amount = 200,000 i= interest rate per period = 0.442 % per month n=total no of payments 360 A=[0.00442*200000*1.00442^360]/(1.00442^360-1) A=1111.11 So monthly installment under first option = $ 1,111.11 c Period Cash flow PV Factor @10% PV of cash flows 1.00 20,000.00 0.91 18,181.82 2.00 19,500.00 0.83 16,115.70 3.00 19,000.00 0.75 14,274.98 4.00 18,500.00 0.68 12,635.75 5.00 18,000.00 0.62 11,176.58 6.00 17,500.00 0.56 9,878.29 7.00 17,000.00 0.51 8,723.69 8.00 16,500.00 0.47 7,697.37 9.00 16,000.00 0.42 6,785.56 10.00 15,500.00 0.39 5,975.92 11.00 15,000.00 0.35 5,257.41 12.00 14,500.00 0.32 4,620.15 13.00 14,000.00 0.29 4,055.30 14.00 13,500.00 0.26 3,554.97 15.00 13,000.00 0.24 3,112.10 16.00 12,500.00 0.22 2,720.36 17.00 12,000.00 0.20 2,374.14 18.00 11,500.00 0.18 2,068.38 19.00 11,000.00 0.16 1,798.59 20.00 10,500.00 0.15 1,560.76 142,567.82 So value of the company = $ 142,567.82 d The compunding factor =20000/10000=2 from FVIF table , the interest rate for compounding fcator of 2 in 5 years is 14.87%
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