Financial Math Answers

A 20 year loan of $50000 is repaid as follows; The borrower pays only interest on the loan, annually in arrears at a rate of 5.5%per annum. The borrower will take out a separate savings policy which involves making monthly payments in advance such that the proceeds will be sufficient to repay the loan at the end of its term. The payments into the savings policy accumulate at a rate of interest of 4%per annum effective. Compute the monthly payments into the savings account which ensure that it contains$50,000 after 20 years, and write down the equation of value for the effective rate of interest on the loan if it is repaid using this arrangement.

An annuity immediate pays$1000 at the end of the first year. The payment increases by 3% per year to compensate for inflation. What is the present value of this annuity on the basis of a rate of 7%, if it runs for 20 years?

Consider an annuity of payments of $1000 at the end of every second year. What is the present value of this annuity if it runs for ten years and the interest rate is 7%?

A borrower agrees to repay a loan of $ 3000 by 15 annual repayments of $500, the first repayment being due after five years. Find the annual yield for this transaction.

A loan of$2400 is to be repaid by 20 equal annual instalments. The rate of interest for the transaction is 10%per annum. Find the amount of each annual repayment, assuming that payments are made
(a) in arrears
(b) in advance

A store increases its prices 10% in each odd month (January, March, May, ...) and
decreases them 10% every even month (February, April, June, ...).
Do prices increase, decrease or stay the same at the end of the calendar year? Justify
your answer with calculations and a clear explanation

John bought a $2,250 lawn mower on an installment plan. installment agreement included 12% down payment in 18 monthly payments of $138 each. How much is the down payment

£250 is invested in a saving account. The nominal rate convertible monthly for the first 3 months is 18% and the nominal rate of interest convertible quarterly for the next 9 months is 20%. How much is in the account at the end of the year?

Rabulani Ltd recently had better than expected earnings which it does not expect to achieve again.
The company wants to distribute 90% of the earnings available to common shareholders for the year through a share repurchase at the current share price, instead of a paying out a dividend. The buy-back will be offset against retained earnings, which comprises nearly the entirety of the company’s equity. The company currently has 10 000 000 shares outstanding trading at R5 each, R60 000 000 in total assets (including the earnings available to common shareholders for the year), R50 000 000 in total liabilities and earnings available to common shareholders is R10 000 000.
Required:
Determine how many shares will be bought back and how the share buy-back would influence the number of shares outstanding in the market. Also discuss the effect the buy-back will have on remaining shareholders if the future earnings available to common shareholders are expected to be a constant R10 000 000 per year.