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1)what is the future value of $ 1700 in 20 years assuming an interest rate of 7 percent compounded semiannually? (Do not round intermediate calculations and round your answer to 2 decimal places,eg
1)what is the future value of $ 1700 in 20 years assuming an interest rate of 7 percent compounded semiannually? (Do not round intermediate calculations and round your answer to 2 decimal places,eg.., 32.16.)
future value
2)Suppose you are a U.S. investor who is planning to invest $315,000 in Japan. You do so at a starting exchange rate of 86.18 ¥/$. Your Japanese investment gains 8.90 percent, and the ending exchange rate is 84.46 ¥/$. What is your total return on this investment?
3)If nominal GDP was reported at $1,427.68 billion and inflation was 4.5 percent, what is the level of real GDP for the period? (Do not round intermediate calculations. Enter your answer in billions rounded to 2 decimal places.)
4)The CPI for this year was reported at 172.65. If inflation was 4.0 percent, what must the CPI have been last year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
5)Union Local School District has a bond outstanding with a coupon rate of 2.9 percent paid semiannually and 24 years to maturity. The yield to maturity on this bond is 2.5 percent, and the bond has a par value of 10,000. what is the price of the bond ?
Expert Solution
1)Future value = present value * (1 + r)n,
where r = semiannual interest rate = 7% / 2 = 3.5%
n = number of semiannual periods = 20 * 2 = 40
Future value = 1700 * (1 + 3.5%)40 = $6,730.74
2)
| Initial Investment in USD = 315,000 |
| Initial Exchange rate = 86.18 ¥/$. |
| 1$ = 86.18 ¥ |
| $315000 = ¥ 86.18*315,000 = ¥ 27,146,700 |
| Initial Investment in Yen = ¥ 27,146,700 |
| Gain = 8.9% |
| Gain = 8.9% * 27,146,700 = ¥ 2,416,056.30 |
| Final investment in Yen = Initial Investment in Yen + Gain |
| Final investment in Yen = ¥ 27,146,700 + ¥ 2,416,056.30 |
| Final investment in Yen = ¥ 27,146,700 + ¥ 2,416,056.30 = ¥ 29,562,756.30 |
| Final exchange rate = 84.46 ¥/$ |
| I$ = 84.46 ¥ |
| 1 ¥ = 1/84.46 $ |
| Final investment in USD = $ 29,562,756.30 * 1/84.46 = $ 350,020.7945 |
| Return on investment = (Final investment/Initial Investment -1 ) * 100 |
| Return on investment = (350,020.7945/315,000 -1 ) * 100 |
| Return on investment = 11.11771253% |
| Return on investment = 11.12% (approx) |
3)Given information:
Nominal GDP = $1,427.68
Inflation rate = 4.5%
Calculations are:
Level of real GDP for the period = Nominal GDP / (1+Inflation rate)
= $1,427.68 / (1+0.045)
= $1,366.20
4)CPI for current year = CPI for last year * (1 + Inflation rate)
172.65 = CPI for last year * (1 + 4%)
CPI for last year = 166.01
5)
Coupon = (0.029 * 10,000) / 2 = 145
Number of periods = 24 * 2 = 48
Rate = 2.5% / 2 = 1.25%
Price of bond = Coupon * [1 - 1 / (1 + r)n] / r + FV / (1 + r)n
Price of bond = 145 * [1 - 1 / (1 + 0.0125)48] / 0.0125 + 10000 / (1 + 0.0125)48
Price of bond = 145 * 35.931481 + 5,508.564886
Price of bond = $10,718.63
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