Question

In 1852​, a person sold a house to a lady for ​$26. If the lady had put the ​$26 into a bank account paying 5​% ​interest, how much would the investment have been worth in the year 2012 if interest were compounded in the following​ ways?

A. monthly
B. continusly

Answer 1

To calculate the value of the investment in the year 2012 with different compounding methods, use the compound interest formula. If the interest is compounded monthly, the investment would be worth $26(1+(0.05/12))^(12 x 160). If the interest is compounded continuously, the investment would be worth $26 x e^(0.05 x 160).

Step-by-step explanation:

To calculate the value of the investment in the year 2012, we need to use the compound interest formula:

A. Monthly Compounding:

Principal(1 + (interest rate/n))^(n x time)

Here, the principal is $26, the interest rate is 5% (or 0.05), n is 12 (since interest is compounded monthly), and the time is 2012 - 1852 = 160 years.

So, the investment would be worth $26(1+(0.05/12))^(12 x 160) in the year 2012 if interest were compounded monthly.

B. Continuously Compounding:

Principal x e^(interest rate x time)

Here, the principal is $26, the interest rate is 5%, and the time is 160 years.

So, the investment would be worth $26 x e^(0.05 x 160) in the year 2012 if interest were compounded continuously.

Answer 2

Step-by-step explanation:

es la b