Question

Please solve using financial calculator only and show work. Thank you.

28. Your brother has asked you to help him with choosing an investment. He has $5,200 to invest today for a period of five years. You identify a bank CD that pays an interest rate of 3.60 percent with the interest being paid quarterly. What will be the value of the investment in five years?

29. Tim has loaned money to his brother at an interest rate of 6 percent. He expects to receive $525 at the end of year one, $650 year two, $850 year three, and $1,000 year four as complete repayment of the loan with interest. How much did he loan out to his brother? (Round to the nearest dollar.)

25. Jack Holmes wants to deposit $5,250 today in a bank account that pays .35 percent monthly. How many years will it take for his investment to grow to $9,500? (Round off to the nearest year.)

26. The risk-free rate of return is currently 3.5 percent, whereas the market risk premium is 9 percent. If the beta of Base Inc., stock is 1.25, then what is the expected return on Base Inc.?

24. John has deposited $3,000 today in an account paying 5 percent interest annually. What would be the simple interest earned on this investment in six years? If the account paid compound interest, what would be the interest-on-interest in six years?

18. You have invested $16,000 of your portfolio in a stock with expected return of 8 percent and $24,000 in a stock with an expected return of 13 percent. What is the expected return of your portfolio?

16. Madison purchased a new car for $29,000. She was allowed $3,000 for her trade in and financed the remainder over 48 months of 4.2% per year. How much is her monthly payment?

7. Ali will invest $2,800 in year one, $3,700 in year two, and $4,900 in year three. If he can earn 7percent on an investment that he makes, what is the future value of his investments at the end of three years?

Answer 1

28) Interest rate = 3.6% per annum

since interest paid quarterly rate per quarter = 3.6 / 4 = 0.9%

number of years = 5

number of periods = 5x4 = 20

FUTURE VALUE = Present value(1+r)ⁿ

here,

r = 0.9% n=20 p.v = 5200

so, F.V = 5200(1+0.9%)²⁰

= $6220.52

29) Here loan amount is the present value of future cash flows discounted at 6%

YEAR CASH FLOW PRESENT VALUE FACTOR @ 6% PRESENT VALUE

1 $525 0.9434 495.285

2 $650 0.890 578.5

3 $850 0.8396 713.66

4 $1000 0.7921 792.1

_{PRESENT VALUE}   $2579.545

25) FUTURE VALUE = P.V(1+r)ⁿ

Here,

future value = $9500 present value = $5250 , r = 0.35% monthly , we need to find n

9500 = 5250(1+0.35%)ⁿ

(1.0035)^n = 1.8095

  PVIFA( r = 0.35% , n = ?) = 1.8095

   by using PVIFA table  

n = 169(approx.)

So Number Of years = 170 / 12 = 14 years(rounded off)

26) Under CAPM method

_{Return(K(e)) = R(f) + B(R(m) – R(S))}

R(f) = risk free rate

R(m) - R(f) = market risk premium

so by using capm method,

Return of base inc. = 3.5 + 1.25(9) = 14.75%

24) simple interest per year = 3000 x 5% =150

for the period of 6 years = 6x150 = $900

for compound intererst we use the formula

F.V. = P.V(1+r)ⁿ

F.V = 3000(1+5%)⁶

=4020.28

Interest = 4020.28 - 3000 = $1020.28 (future value - present value)

18) Expected return on portfolio = weighted average return of individual securities

=W₁* R₁ + W₂*R₂

total value of portfolio = 16000+24000 = $40,000

W₁ = 16000 / 40000 = 0.4 , R₁ = 8%

W₂ = 24000 / 40000 = 0.6 , R₂ = 13%

So return on portfolio = 0.4*8% + 0.6*13% = 11%

Return = 40,000*11% = $4,400

16) Value of car = $29,000

Trade in = $3,000

Balance =  $26000 (loan amount)

n = 48 months, r = 4.2% per year, since it is monthly it will be 4.2 / 12 = 0.35%

monthly payments = loan amount / PVIFA(r = 0.35% , n = 48)

PVIFA(r = 0.35% , n = 48) = 44.1138

monthly payments = 26000 / 44.1138 = $589.38

7) Amounts are invested at the end of year

FUTURE VALUE = P.V(1+r)ⁿ

for the investment that made at the end of year 1( p.v = 2800 , r = 7% , n = 2 years)

F.V = 2800(1+7%)²

= $3205.72

for the investment that made at the end of year 2 (p.v = 3700 , r = 7% , n = 1 year)

F.V = 3700(1+7%)¹ = $3959

there will be no interest accrued for the investment that made at the end of third year

so F.V = P.V =$4900

Total value = 3205.72+3959 +4900

= $12064.72