Question

Your grandmother just gave you ​$5 comma 000. ​You'd like to see what it might grow to if you invest it.

a. Calculate the future value of ​$5 comma 000​, given that it will be invested for 5 years at an annual interest rate of 6​%.

b. Recalculate part ​(a​) using a compounding period that is semiannual​ (every six​ months).

c. Now​ let's look at what might happen if you can invest the money at an annual rate of 12​% rate rather than a 6​% ​rate; recalculate parts ​(a​) and ​(b​) for an annual interest rate of 12​%.

d. Now​ let's see what might happen if you invest the money for 12 years rather than 5 ​years; recalculate part ​(a​) using a time horizon of 12 years​ (annual interest rate is still 6​%).

Answer 1

Solution. Your g on. Your grand mother gave you $5000 You want to know how much it will grow if you invest it. So, here we will use compounding technique. So, Present Value = $5,000 a calculate future Value $500o invested for 5 years at by interest rate per annum. 2 rate of interest t= time Future value (eu)- Present Value (Puslitry - 5000 lit for you = 5000[140.0675 z 5000 1.0635 = 5000[1-33822558] = $6691.1979 = $6691.13 (approx) O calculate future Value 4 $5000 invested for 5 years at 6y interest rate, compounded semiamudly. -Solution. As the interest is calculated semi annually so, interest rate will be divided by 2 and time (in years) will be multiplied by 2 as interest is calculated a times in a year

So, - ra 6% 3% and and time (t) = 549 time ( 10 hof-yeary Fve 5,000 [i+ ]" = 5000f 1.037'' 5000[1.843916587 F 6769.5819 = $ 6714.58 (approx) Annual R nterest -12% Time = 5 years Compounded Annually of as calculated in part (ast Future Value. (PU)> 5000[1 + 1975 z 5000[1-1975 = 5000[1.76234168] > $88 11.7084 - $8811•7) compounded semi-annually of as calculated in part 67 Rate of interest (8)= 1 / 2 640 per half-year E = = = = = =

id) . Time (t) = 5x2 . i lo hall-years so, fu= 50001 1+ teo] 2 5000[1.00]" - 5000$ 1.7908477] 2$8954.2385 3 $ 8954.24 (ao prox) Time = 12 years Rate of Interest (8)= 6 % per annum. Compounded Annually [as in pointla)] FV = 5000| ?+ = 5000[4.067 = 5000[2.01219647 2 10,060,9824 12 $10,060.98 Copprox) I have used calculator for these calculations, you can even use compounding or future value tables for these so, 7 12