How Long to Double Your Money with Compound Interest?

AI Thread Summary
To determine how long it takes for $30,000 to double at an interest rate of 4.3% compounded annually, the formula S(1 + r)^n can be used, where S is the initial amount, r is the interest rate, and n is the number of years. Setting the equation to 2S allows for solving for n, leading to the conclusion that the investment will double in value. The compounding effect can be observed through the pattern of increasing amounts each year, specifically $30,000 multiplied by (1.043)^n. This method highlights the importance of understanding compound interest in financial calculations. The discussion emphasizes the necessity of familiarizing oneself with relevant formulas to solve such problems effectively.
jahaddow
Messages
47
Reaction score
0
A fixed deposit investment attracts interest of 4.3% p.a. compounded annually. How long will $30 000 take to double in value?
 
Physics news on Phys.org
jahaddow said:
A fixed deposit investment attracts interest of 4.3% p.a. compounded annually. How long will $30 000 take to double in value?

What have you tried? What are the relevant equations?
 
This is all I know, I don't know what method should be used to find the answer?
 
That's very peculiar! If you aren't taking a course that has discussed "compound interest", why have you been assigned a problem like this? If you are then surely there are formulas for compound interest in your textbook aren't there?

If I remember correctly, after n years, an amount S at r rate of interest (so that 100r% is the annual percentage rate) compounded annually is given by S(1+ r)^n. Set that equal to 2S, cancel the "S"s and solve for n.
 
A powerful strategy is to think about the specific case and try to obtain a general equation.

The first year, you have $30 000

The second year it is compounded by $30 000 x .043 so you have 30 000 + 30 000 x .043
= 30 000 (1.043)

The next year your money increases again by 30 000 (1.043) (.043) for a total of 30 000 (1.043) + 30 000 (1.043) (.043) = 30 000 (1.043) (1.043) = 30 000 (1.043)^2

By now you should have noticed a pattern.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Similar threads

Compound Interest Homework: Amy vs Bob
Replies
8
Views
3K
Logarithm: Compound interest problem
Replies
2
Views
3K
Compound Interest Systems of Equations Problem
Replies
29
Views
4K
Problem on interest rates -- Math proof interesting
Replies
2
Views
3K
Geometric Sequence to solve an Interest Problem
Replies
2
Views
1K
Logarithm question using compound interest formula
Replies
4
Views
3K
MHB Simple Interest Investment: How Long Will It Take to Grow $550,000 to $720,000?
Replies
1
Views
1K
How Much Will Mike Save by Age 60 With a Growing Salary and Fixed Savings Rate?
Replies
3
Views
4K
Solving trigonometric equations using compound angle formula
Replies
7
Views
5K
Interest Theory- Annuity Withdrawals
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top