Lynne invested $35,000 into an account earning 4% annual interest compounded quarterly. She makes no other deposits into the account and does not withdraw any money. What is the balance of Lynne's account in 5 years?

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04-01-2017
Mathematics

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Lynne invested $35,000 into an account earning 4% annual interest compounded quarterly. She makes no other deposits into the account and does not withdraw any money. What is the balance of Lynne's account in 5 years?

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dexteright02 dexteright02 · Answer 1 · 2017-01-04T16:36:06-05:00

Data:
P = 35000
r = 4% = 0,04
n = 4
t = 5
P' = ?
I = ?

We have the following compound interest formula

$P' = P*(1+\frac{r}{n})^{nt}$

$P' = 35000*(1+\frac{0,04}{4})^{4*5}$
$P' = 35000*(1+0,01)^{20}$
$P' = 35000*(1,01)^{20}$
$P' = 35000*(1.22019003995...)$
$P' \approx 42,706.66$

So the new principal $P'$ after 5 years is approximately $42,706.66.

Subtracting the original principal from this amount gives the amount of interest received:

$P' - P = I$

$42,706.66 - 35000 = \boxed{7,706.66}$

astha8579 astha8579 · Answer 2 · 2022-03-04T00:47:43-05:00

The interest earned on the amount will increase the net balance. The balance of Lynne's account in 5 years would become $76,689.31 approximately.

How to calculate compound interest's amount?

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that simple interest, then the interest amount earned is given by:

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And thus, final amount will be:

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For the given case, the principal amount (initial amount) Lynne invested is P = 35000 (in dollars)

The rate of interest = 4% compounding quarterly.

Here, unit of time is is quarter of an year which means 1/4 of an year.

The time is given to be 5 years. In each year, there are 4 quarters, so in 5 years, there would be 20 quarters of years.

Thus, T = 20 (we always need to keep unit of time same for R and T for using that formula).

Putting these values in the above formula, we get the final amount's value in Lynne's account in 5 years as:

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Thus, the balance of Lynne's account in 5 years would become $76,689.31 approximately.

Learn more about compound interest here:

https://brainly.com/question/11897800