Financial Math Answers

Both Maria and Firdaus are salaried individuals. They are saving for their retirement 20 years from now. Both of them are also in the 28% marginal tax bracket. Maria makes a $2000 contribution annually on December 31 into a savings account (subjected to tax) earning an effective rate of 8% per year. At the same time, Firdaus makes a $2000 annual payment to an insurance company (tax-sheltered) for an after-tax-deferred annuity. The annuity also earns interest at an effective rate of 8% per year. (Assume that both of them remain in the same tax bracket throughout this period, and disregard state income taxes.)

Calculate how much each of them will have in their investment account at the end of 20 years.

Compute the interest earned on each account.

Show that even if the interest on Firdaus’ investment were subjected to a tax of 28% upon withdrawal of his investment at the end of 20 years, the net accumulated amount of his investment would still be greater than the net accumulated amount of Maria’s investment.

(i) Express 5% pa effective interest as a nominal annual interest rate convertible quarterly.

(ii) Find the annual effective interest rate equivalent to a nominal interest rate of 12% pa convertible four-monthly.

Which has the higher annual yield, 6% compounded quarterly or 6.25% compounded semiannually?

A retired couple have a fixed income of P3500 per month. Assuming an annual inflation rate of 7%,

what is the purchasing power of their monthly income in 5 years?

A retired couple have a fixed income of P3500 per month. Assuming an annual inflation rate of 7%,

what is the purchasing power of their monthly income in 5 years?

Un solde de prix de vente a été consenti aux conditions suivantes :

• Montant : 40 000 $
• Amortissement : 10 ans
• Terme : 24 mois
• Taux d’intérêt : 6 % (capitalisation trimestrielle)
• Versement : mensuel
• Déterminez les obligations résultant de ce solde de prix de vente.

A sale price balance has been granted on the following conditions: amount: $40,000; amortization: 10 years; term: 24 months; interest rate: 6% (a quarterly compounding); installment: monthly. Determine the obligations resulting from this sale price balance.

George Drug Products Ltd (GDPL) is faced with several possible investment projects. For each, the total cash outflows required will occur in the initial period. The cash outflows expected net present values and standard deviations are as follows:

Project Cost Sh. ‘000’ Net present value Standard deviations

A 10,000   1,000         2,000

B  5,000             1,000                   3,000

      C               20,000             2,500                  1,000

D                1,000               500                  1,000

E               50,000              7,500                  7,500

All projects have been discounted at a risk-free rate of 8% and it is assumed that the distribution of their possible net present values are normal.

(a) Construct a risk profile for each of these projects n terms of the profitability index     (8 marks)

(b) Ignoring size problems do you find some projects clearly dominated by others? (7 marks)

7. A bond has a P15,000 face value, a 4-year maturity, and a 3.5% coupon. What is the total of the interest payments paid to the bondholder? Show your solution.

6. Suppose you bought 300 shares of Barney’s Burger at the 52-week low and sold the shares at the 52-week high. Suppose the selling price per share was P7.47 and the purchase price per share was P2.56.

(a) Ignoring dividends, what was your profit or loss on the sale of stock?

(b) If your broker charges 2.1% of the total sale price, what was the broker’s commission? Round to the nearest cent.

Show your solutions.

5. A stock pays an annual dividend of P0.82 per share. The stock trading is at P51.25. Find the dividend yield. Show a solution.