Choice a is the correct answer for the question
Answer:
<em>P'=2,367 million $</em>
Step-by-step explanation:
<u>Compound Interest
</u>
It refers to the case where the interests earned in a certain period are added to the principal sum of a loan and re-invested. Interest in the next period is then earned on the principal sum plus previously accumulated interest.
Being P the principal, or initial amount of a loan or deposit, r the nominal annuual interest rate and t the time the interest is applied, the total accumlated value or future value is
![{\displaystyle P'=P\left(1+{\frac {r}{n}}\right)^{nt}}](https://tex.z-dn.net/?f=%7B%5Cdisplaystyle%20P%27%3DP%5Cleft%281%2B%7B%5Cfrac%20%7Br%7D%7Bn%7D%7D%5Cright%29%5E%7Bnt%7D%7D)
According to the conditions of the problem, Christopher deposited 1 billion into his savings. This gives us the principal P=1,000 milion dollars. The interest rate is 9% compounded once a year during t=10 years. Here n=1 since the compounding does not occur in the middle of the yearly period. Thus
![{\displaystyle P'=1,000\left(1+{\frac {0.09}{1}}\right)^{1\times 10}}](https://tex.z-dn.net/?f=%7B%5Cdisplaystyle%20P%27%3D1%2C000%5Cleft%281%2B%7B%5Cfrac%20%7B0.09%7D%7B1%7D%7D%5Cright%29%5E%7B1%5Ctimes%2010%7D%7D)
![\boxed{P'=2,367\ million\ \$}](https://tex.z-dn.net/?f=%5Cboxed%7BP%27%3D2%2C367%5C%20million%5C%20%5C%24%7D)