Compound Interest

[m_photographer]

I missed these two problems on a quiz and cannot figure out what I did wrong...

A) Suppose that $980 is invested at 7.24% compounded continuously. How much is in the account after 14 years? Round your answer to the nearest cent.

I used the formula A= P(1+r/n)^nt

This gave me A= 980 (1+0.0724/365)^5,110

Therefore, my final answer was $2,700.12



B) Suppose that $897 is invested at 5.25% interest compounded quarterly. How much is in the account after 13 years? Round your answer to the nearest cent.

I used the same formula as in the one above except n=4 in this one instead of 365.

This gave me A= 897 (1+0.0525/4) ^ 52

My final answer was $1,767.14


​Please help me find my mistakes.

 

[JeffM]

I missed these two problems on a quiz and cannot figure out what I did wrong...

A) Suppose that $980 is invested at 7.24% compounded continuously. How much is in the account after 14 years? Round your answer to the nearest cent.

I used the formula A= P(1+r/n)^nt

This gave me A= 980 (1+0.0724/365)^5,110 This gives you DAILY compounding, not continuous compounding.

The formula you need is \(\displaystyle \displaystyle A = 980 * \lim_{n \rightarrow \infty}\left\{\left(1 + \dfrac{r}{n}\right)^n\right\}^{14} = 980 * (e^r)^{14} = 980 * e^{14r} = 2,700.39.\)

This formula OUGHT to be in your book, but you can find it at wikipedia.

Therefore, my final answer was $2,700.12



B) Suppose that $897 is invested at 5.25% interest compounded quarterly. How much is in the account after 13 years? Round your answer to the nearest cent.

I used the same formula as in the one above except n=4 in this one instead of 365.

This gave me A= 897 (1+0.0525/4) ^ 52

My final answer was $1,767.14

I get the same answer.​ Are you sure that there is not some aspect to the problem that you may have overlooked?

Please help me find my mistakes.

.

 

[lookagain]

.

I used the formula > > > A= P(1+r/n)^nt < < <

I used the same formula as in the one above except n=4 in this one instead of 365.
> > > ​Please help me find my mistakes. < < <

Here is a mistake. Regardless that you applied the intended formula with the
correct product, nt when you type the exponent expression, it must be in
grouping symbols, such as:


A = P(1 + r/n)^(nt)


On a calculator that shows the symbols on the screen, (, ), /, ^, *,
type in these two expessions (with specific numbers for each variable)
and compare the values for:


P(1 + r/n)^n*t


P(1 + r/n)^(n*t)