Lux Investing

What is the future value of $250,000 invested at a continuously compounded annual rate of 5%, after 3 years?

Round to the nearest dollar

Public Comments

1. The answer is 250000*(1.05^3)=$289,406
2. $289,406
3. its 250000 * e^(0,15) = 290458,5607 In general: Investment * e^(interest rate * years)
4. $290,459 is the nearest integer to 250,000 * exp(0.05 * 3) = 290,458.56....
5. A=P(1+(i/q)))^nq = 290456
6. Given:P=$250,000 R=5% T=3 YEARS.AND COMPOUNDING IS EVERY YEAR. Let us calculate future value after 1 year. Interest=P*R*T/100 =250000*5*1/100 =12500$ PRINCIPLE AMOUNT FOR SECOND YEAR=250000+12500=262500$ Let us calculate future value after 2 ND year. Interest=P*R*T/100 =262500*5*1/100=13125$ PRINCIPLE AMOUNT FOR 3RD YEAR=262500$+13125$=275625$ Let us calculate future value after 3RD year. Interest=P*R*T/100=275625*5*1/100=13781.25 SO,TOTAL AMOUNT AFTER 3 YEARS=289406.25$
7. Amount= P(1+R/100)*n = 250000(1+5/100)*3 = 250000(1+0.05)*3 = 250000(1.05)*3 = 250000X1.157625 = 2892406.25 = $2,892,406(approx)
8. Continous Compound Interest Formula I = Pe^(rt) I = 250000 * e^(.05 * 3) I = 250000 * e^(.15) I = $290459
9. Let P= the amount of the investment=$250,000 At the end of the first year, the investment P including interest will amount to: P+Pi where i is the compounded annual rate Factoring out P from the above expression, we get: P(1+i) At the end of the second year, the investment P will amount to: P(1+i)+ P(1+i)i Factoring out P(1+i) from the above expression we get: P(1+i)(1+i)= P(1+i)^2 At the end of the third year, the investment P including interest will amount to: P(1+i)^2+(P+i)^2i Factoring out P(1+i)^2 from the above expression we get: P(1+i)^2(1+i)= P(1+i)^3 Now substitute in the above expression the given value of P and i: 250000(1+5/100)^3= 250000(1+.05)^3= 250000(1.05)^3= 250000(1.157625)= $289,406.25 Note that 5% can be written as 5/100 or .05. If you noticed we have derived a compound interest formula. For an investment P at an annual interest rate i , at the end of n years, the total investment will amount to P(1+i)^n. In the above problem n=3. But if deriving a formula is too much for you, then solve the problem step by step, i.e. at the end of the 1st year, how much will the total investment be; at the end of the 2nd year, how much will the total investment be; and at the end of the 3rd year, how much will the investment be. That will be a very tedious process. Can you imagine how long it will take you to solve a problem if say the number of years is changed to 10 instead of 3? So, simplify and learn to derive a formula.
10. A=p(1+r/100)^n =250000(1+.05)^3 =250000*1.05^3 =289406.25$