Consider an investment of $1,000. (a) Using a financial calculator, calculate th
ID: 2722400 • Letter: C
Question
Consider an investment of $1,000.
(a) Using a financial calculator, calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 2% per annum compounded annually. Round your answer down to the nearest year.
(b) Using a financial calculator, calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 5% per annum compounded annually. Round your answer down to the nearest year.
(c) Using a financial calculator, calculate the time taken for this investment to treble in value to $3,000 at an interest rate of 10% per annum compounded annually. Round your answer down to the nearest year.
(d) Using your answers to (a), (b) and (c), write down a simple mathematical formula for trebling time T years in terms of the annual interest rate i % with annual compounding. Do not use the logarithmic (log) function in your formula. Your formula should be valid for low interest rates. Illustrate that your formula works for i=2, i=5 and i=10.
(e) Some analysts predict that property prices in some parts of Australia treble approximately every 15 years. Using your answer to (d), what would be the approximate annual rate of return for property investors in this situation?
Explanation / Answer
For an initial Investment to treble,ie. Become 3 times a)Compounded @ 2% p.a. Using the formula to compound the principal, A=P(1+i)^n A= amount;P=Principal/Initial investment;i= interest rate;n= no.of compounding periods/Years 3000=1000(1+0.02)^n No.of Years,n= 55.478 Years b)Compounded @ 5% p.a. 3000=1000(1+0.05)^n n= 22.517 Years c)Compounded @ 10% p.a. 3000=1000(1+0.10)^n n= 11.527 Years d. P Int.I No.of yrs.N Amount 1000 2% 55 3000 1000 5% 23 3000 1000 10% 12 3000 Keeping 2% and 55 years as base, When I is doubled (5%) n is halved( 23) (Diff. due to rounding off) When I is multiplied by 5 (10%) n is divided by 5(11) When I is divided by that no. N needs to be multiplied by the same no. FORMULATING, we have the equation 3x=x(1+i/n)^(1*n) where x= initial investment i= interest rate n= compounding periods/times 3x= final amount APPLICATION With rounding off answers With actual decimals 1000(1+0.02)^55 1000(1+0.02)^55.478 2972 3000 1000*(1+(0.02*2.5))^(55/2.5) 1000*(1+(0.02*2.5))^(22.517) 2925 3000 1000*(1+(0.02*5))^(55/5) 1000*(1+(0.02*5))^(11.527) 2853 3000