Question for people with knowledge on economics.?

Question

Which would you rather have, if you have only 2 options: $100 in 8 years from now at a 2 percent interest or $100 in 2 years if the interest rate is 8 percent. And can also explain me why? Using economics calculations. Thanks.

Answer 1

Knowledge in economics tries first to find out what the meanng of the question and then tries to solve. Your question is not clear as to what is being offered. I will take three alternative meaning of the offer and solve:

A. The offer is of a $100 Loan: one repayable with cumulative interest at a rate of 2% per annum at the end of 8 years and the other repayable with cumulative ineterest at a rate of 8% at the end of the second year. Clearly I will prefer the 2% * year loan as I would have to pay after a longer period, besides the fact that the repayment amount in the 8th year-end is $117.1659381 as against $116.64 in the 2nd year-end: while I pay a little higher total amount in the first option, in present value terms  ( assuming a small discount rate of even 2 percent) the real value of total amount to be paid back is much lower than in option 1.

B. The offer is of a prize of Rs 100 bank deposits - one earning interest at a rate of 2% per year encashable at the end of 8th year along with cumulative interest and the other earning interest at the rate of 8% per year encashable after 2 years along with cumulative interest. Clearly, the 2 year 8% interest bank deposit is the best option because it gives me $116.64 after 2 year as compared $117.17 AFTER 8 YEARS.

The present value of $166.4 after two years is greater than $117.17 at a discount rate of even 2%. Just to put it another way, I get $116.64 after two years at put it 1.5% interest for 6 years , my money will grow to much more than $117.17.within the total 8 year period.

C. This is what you are probably asking. The option is to get a prize of $100 after 2 years.if the interest rate ruling in the market is 8% and a prize of $100 after 8 years i tre rukling market interest rate is 2% per annum. In this case we have to find ou the present value of the prizes using the interest rate relevant for discounting. The present value of the first prize when interest rate is 8% is $100/1.1664 = $85.73388203 or $85.73 approx. whereas the present value of the prize when interest is 2% $100/1.11717 = $85.3490371 or approximately $85.35 Clearly the 2-year 8% prize is preferable.

For Compunding the values you have to use the formula;

100* (1.02)^8 and 100*(1.0*)^2  where ^ implies power of the figure in (), ie. multiplying the figure itself the number of times shown inside the bracket.

For discounting, you use the formula

100/(1.02)^8  and 100/(1.08)^2