Question

in 1886, a person sold a house to a lady for $30. if the lady had put the $30 into a bank account paying 6% interest, how much would the investment have been worth in the year 2011 if interest was 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.)

Explanation:

Step1: Calculate the number of years

The number of years \(t = 2011 - 1886=125\) years.

Step2: Use the compound - interest formula for monthly compounding

The compound - interest formula is \(A = P(1+\frac{r}{n})^{nt}\), where \(P=\$30\), \(r = 0.06\) (since \(6\%=0.06\)), \(n = 12\) (monthly compounding).
Substitute the values: \(A=30(1 +\frac{0.06}{12})^{12\times125}\).
First, calculate \(\frac{0.06}{12}=0.005\) and \(12\times125 = 1500\).
Then \(A = 30(1.005)^{1500}\).
Using a calculator, \((1.005)^{1500}\approx442.5926\).
So \(A=30\times442.5926=\$13277.778\approx\$13278\).

Answer:

\(13278\)