Question

You have just been notified that you are the only living descendent of a math-loving eccentric, who put $10 in a bank account in 1800 and left it. Since then, the money has been collecting interest. He left instructions in his will that in the year 2019, if he had any living descendant who could determine the exact amount of money in the bank, that person could have the money. If not, the account was to be turned over to charity. Can you claim the money? Here is the information: The $10 was deposited April 30th, 1800, (Wow!!! That's today's date!!! That should make it easier, right??...Don't overthink the compounding!!) in a bank account that has an annual interest rate of 5%. Since then, the interest has been compounded quarterly. If you are correct in calculating the balance as of April 30th, 2019, you can have the money. On that day, how much money will be in the account? Express your answer to the nearest penny. Show all of your work clearly.

Answer 1

Answer:

$\ 532,166.99 \text{ (to the nearest penny)}$

Step-by-step explanation:

$Amount \: at \: Compound \: Interest= P(1+\frac{r}{k} )^{nk}$

Principal, P=$10

Rate,r =5%

Compounding Period,K=4 (Quarterly)

Number of Years, n=2019-1800=219 Years

$\text{Balance as at April 30th 2019}= 10(1+\frac{0.05}{4} )^{219*4}\\=10(1+0.0125 )^{876}\\=10(1.0125 )^{876}\\\approx\ 532166.99 \text{ (to the nearest penny)}$