General Maths Question (1 Viewer)

[StephCarmen]

Theo invests a sum of money in an account at an interest rate of 7.5% per annum. The time taken, n, for Theo's investement to double in value can be found by solving the equation (1.075)<SUP>n </SUP>= 2

(i) Use the method of substitutio to find the solution to this equation, correct to the nearest whole number.

(ii) Write an equation that when solved will determine the length of time for an account of money to reble when invested at 15% per annum. (Do not actually solve the equation)

(iii) Write an equation and solve it to find the length of time it takes for an item to fall to less than one quater of its intital value when it depreciates at the rate of 25% per annumm.


The test has been done. But this was one question i really struggled on.
I was advised that part (i) was done by trial and error which is correct but i do not know how to do the other parts.

 

[PC]

Theo invests a sum of money in an account at an interest rate of 7.5% per annum. The time taken, n, for Theo's investement to double in value can be found by solving the equation (1.075)<SUP>n </SUP>= 2

(i) Use the method of substitutio to find the solution to this equation, correct to the nearest whole number.

You can also solve this equation by taking the log of both sides (if that's your thing), or if you have a graphic calculator, use the "Solver" function in the "Equa" mode.

Most people will use trial and error, or guess and refine as it's now called.

When n = 2, 1.075² = 1.155625
When n = 4, 1.075⁴ = 1.335469141
When n = 8, 1.075⁸ = 1.783477826
When n = 9, 1.075⁹ = 1.917238662
When n = 10, 1.075¹⁰ = 2.061031562

So it will take 10 years for the investment to double in value.

(ii) Write an equation that when solved will determine the length of time for an account of money to reble when invested at 15% per annum. (Do not actually solve the equation)

Since the investment is made at a rate of 15% p.a., and we're compounding, this represents an increase of 15% every year or 115% (or 1.15) of the principal every year.

Equation: 1.15ⁿ = 3

(iii) Write an equation and solve it to find the length of time it takes for an item to fall to less than one quater of its intital value when it depreciates at the rate of 25% per annumm.

Similarly: 0.75ⁿ = 0.25

Hope this helps.

 

[StephCarmen]

Yeah it does. Thanks!
I have a graphics calculator..but i hate using it. I don't know why...it just annoys me.