# Boas 1.13 Compound interest/geometric series

• I
• Battlemage!
In summary, the problem asks for the amount of money one would have after investing $10 at the beginning of each month for 10 years at a 6% interest rate compounded monthly. The formula for this is given as (1.005)n dollars after n months. Using this formula with a=10.05, r=1.005, and n=120, the result is approximately$1646.99. However, compound interest calculators give different numbers, possibly due to different compounding frequencies.
Battlemage!
From Mary Boas' "Mathematical Methods in the Physical Sciences" Third Edition.

I'm not taking this class but I was going through the textbook and ran into an issue. The problem states:

If you invest a dollar at "6% interest compounded monthly," it amounts to (1.005)n dollars after n months. If you invest $10 at the beginning of each month for 10 years (120 months), how much will you have at the end of the 10 years?​ Now, the problem expects you to use the formula for partial sum of a geometric series. $$S_n=\frac{a(1-r^n)}{1-r}$$ So, as far as I can tell, the series is $$10*1.005+10*1.005^2+10*1.005^3+...$$ which would mean: a = 10*1.005 = 10.05, r = 1.005, and n = 120.​ Computing Sn with those values gives about$1646.99.

Interestingly, Quora gave the exact same answer: https://www.quora.com/Investing-que...much-will-you-have-at-the-end-of-the-10-yearsMy problem? Compound interest calculators give a totally different number. For example:
http://www.bankrate.com/calculators/savings/compound-savings-calculator-tool.aspx
gives $2014. screencap: https://s15.postimg.org/gxaujjt8b/compoundinterest1.jpg https://www.investor.gov/additional...l-planning-tools/compound-interest-calculator gives$2013.46.
screencap: https://s17.postimg.org/4ai0gb7xb/compoundinterest2.jpg

So, I am kind of lost here. Did I do the problem wrong? If so please enlighten me. I double checked their value of 1.005 using (1+r/n)nt; (1 + 0.06/12) = 1.005, so 1.005n appears to be valid to me.Any suggestions?

Think about the differences among annual/yearly, monthly (which you've got), and "continuous" compounding.

## 1. What is compound interest?

Compound interest is a type of interest that is calculated not only on the initial principal amount, but also on the interest earned from previous periods. This means that the interest grows over time, leading to a higher return on investment.

## 2. How is compound interest different from simple interest?

Simple interest is calculated only on the initial principal amount, while compound interest takes into account the accumulated interest from previous periods. This means that compound interest will result in a higher return on investment over time.

## 3. What is a geometric series?

A geometric series is a series of numbers where each term is found by multiplying the previous term by a constant ratio. In the context of compound interest, the constant ratio represents the interest rate.

## 4. How is compound interest calculated?

Compound interest is calculated using the formula A = P(1+r)^n, where A is the final amount, P is the principal amount, r is the interest rate, and n is the number of compounding periods. This formula takes into account the effect of compounding on the principal amount.

## 5. How does the frequency of compounding affect compound interest?

The more frequently compounding occurs, the higher the interest earned will be. This is because with more frequent compounding, the interest is added to the principal amount more often, leading to a higher accumulated interest and a higher return on investment.

Replies
13
Views
2K
Replies
2
Views
1K
Replies
9
Views
2K
Replies
2
Views
10K
Replies
3
Views
1K
Replies
2
Views
2K
Replies
12
Views
11K
Replies
8
Views
3K
Replies
2
Views
1K
Replies
2
Views
1K