in 1859, a person sold a house to a lady for $26. if the lady had put the $26 into a bank account paying 5%…

in 1859, 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 2011 if interest were compounded in the following ways? a. monthly b. continuously a. if compounded monthly, the investment would be worth $ in 2011. (round to the nearest dollar as needed.)

in 1859, 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 2011 if interest were compounded in the following ways? a. monthly b. continuously a. if compounded monthly, the investment would be worth $ in 2011. (round to the nearest dollar as needed.)

Answer

Explanation:

Step1: Calculate the number of years

The time period from 1859 to 2011 is (t = 2011 - 1859=152) years.

Step2: Use the compound - interest formula for monthly compounding

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (P=$26), (r = 0.05) (since (5%=0.05)), (n = 12) (monthly compounding). Substitute the values into the formula: [ \begin{align*} A&=26(1 +\frac{0.05}{12})^{12\times152}\ &=26(1+\frac{0.05}{12})^{1824}\ \end{align*} ] First, calculate (\frac{0.05}{12}\approx0.004167), then (1+\frac{0.05}{12}\approx1.004167) ((1.004167)^{1824}\approx12730.67) (A = 26\times12730.67=$331007.42\approx$331007)

Answer:

(331007)