70 70 newvalue initialvalue x Ty new value = initialvahie× 2 Another model for e

Question

70 70 newvalue initialvalue x Ty new value = initialvahie× 2 Another model for exponential growth: Doubling Time formula (and for decay: Half-life formula) 4. Calculate Taxable for Nigeria in problem #1 on reverse. 5. Use this Tsouble and the formula above to calculate the population of Nigeria in ten years. How does this compare to the prediction you made using the Compound Interest formula? 6. Calculate Tdouble for the world population, using the 1963 growth rate. 30 yeas Lokat your graph you made on reverse. On the graph, does the population doublen the time you calculated in the previous question? (Please explain with "It went from about...to about..." 7. 8. Does the world population today match the predictions you made in the graph? Why or Why notn no, the times are chagiy, le 9. If an investment is made at 5% annual compound interest, about how long will it take for your money double? 10. If my investment doubles in about 20 years, what is the approximate interest rate? 11, worldwide oil consurmption is increasing at a rate of 2.1% per year. In how many years will our consumption double? 11b. By what factor will oil consumption increase in a decade? (hint: try some number as an "initial valu find the new value, then...) 12. The half life of a drug in the bloodstream is 4 hours. By what factor does the concentration of the d decrease in 24 hours? In 36 ho

Explanation / Answer

Question: If an investment is made at 5% annual compound interest, about how long will it take for your money to double.

Solution:

The Accrued Amount (Investment + Interest) at the end of 't' years for an investment of 'I' with an annual interest of r% is given by:

A = P*(1+r)t

Given r = 0.05, we need to find t when A = 2*P (Doubling the investment).

2P = P* (1+0.05)t

(1.05)t =2P/P = 2.

By applying Log to the base of 1.05 on either sides,

Log1.05 (1.05)t = Log1.05 2

t = Log1.05 2 (which can be evaluated in Excel using the formula: =LOG(2,1.05))

t = 14.2067 or 14 years and (0.2067*12) months

So, the investment made at 5% annual compound interest will double in 14 years and 2.5 months

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