Mathematics of Finance
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Final answers should be rounded to the nearest cent (two decimal places). Beware of rounding intermediate results.
1. A resident of the United States has a base income of $23,000 after adjustments for deductions. New legislation by Congress would tax this income at a rate of 11 percent. What tax would be due?
2. Find the simple interest on $8537 at 10% per annum for 8 months.
3. Find the simple exact interest on $24,281 at 12 3/4% (per annum) from June 8 of one year to February 14 of the next year.
4. Find the effective rate corresponding to 3% compounded quarterly.
5. What is the ending balance from an initial deposit of $5,000 at 14% compounded monthly for 4 years?
6. Find the amount of interest earned on a deposit of $1,609.25 at 13% compounded monthly for 90 months.
7. Find the present value of $10,425 in 39 months at 13.75% compounded monthly.
8. Find the value of an annuity where $275 is deposited at the end of each quarter for 3 years and the interest rate is 9.5% compounded quarterly.
9. Determine the amount of each payment to be made to a sinking fund with 10 annual payments compounded at 14% annually, in order that enough money will be available to pay off a loan of $5,000.
10. Find the present value of an ordinary annuity with monthly payments of $274.14 for 48 months at 12% compounded monthly.
EC. An alumnus wants to set up a trust (which earns 9% interest compounded semiannually) to provide a grant to his alma mater of $10,000 every six months, beginning six months from now, for six years. How much should be deposited in the trust?
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1. A resident of the United States has a base income of $23,000 after adjustments for deductions. New legislation by Congress would tax this income at a rate of 11 percent. What tax would be due?
11% of 23000 is 23000 x 11/ 100 = 230 x 11 = $2530
2. Find the simple interest on $8537 at 10% per annum for 8 months.
The simple interest formulate is
I = PTR/100 where P is principal , R is rate of interest and T is time in years.
In our problem, P = 8537
R = 10
T = 8 months = 8/12 = 0.666 years
Hence interest is 8537 x 0.1 x 0.666 = 560.1333333 or 569.13 when rounded to 2 decmial points
3. Let us assume that a year has 365 days. Interest rate for 365 days = 12 3/4 % or 12.75 %
Total number of days from June 8th to February 14th is
Days of June + July + August + September + October + November + December + January + Februray
This is equal to:
23 + 31 + 31 + 30 + 31 + 30 + 31 + 31 + 14 = 252
Time = 252/365 = 0.69041095
Interest = P x T x R/100 = 24281 x 0.69041095 x 12.75/100 = 2137.3932053 or 2137.39 when ...
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