eli invested $31,000 in an account paying an interest rate of 4.3% compounded monthly. assuming no deposits…

eli invested $31,000 in an account paying an interest rate of 4.3% compounded monthly. assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 7 years?

eli invested $31,000 in an account paying an interest rate of 4.3% compounded monthly. assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 7 years?

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (P) is the principal amount, (r) is the annual interest rate (in decimal form), (n) is the number of times interest is compounded per year, and (t) is the number of years.

Given that (P=$31000), (r = 4.3%=0.043), (n = 12) (compounded monthly), and (t = 7) years.

Step2: Substitute the values into the formula

Substitute the values into the formula: [ \begin{align*} A&=31000\left(1 +\frac{0.043}{12}\right)^{12\times7}\ &=31000\left(1+\frac{0.043}{12}\right)^{84} \end{align*} ]

First, calculate (\frac{0.043}{12}\approx0.003583). Then (1+\frac{0.043}{12}\approx1.003583).

Next, calculate ((1.003583)^{84}). Using a calculator, ((1.003583)^{84}\approx1.357)

Step3: Calculate the final amount

Then (A = 31000\times1.357 = 42067)

Answer:

(42100) (rounded to the nearest hundred dollars)