Congratulations! You were the 10th caller on the KMTH morning show and you just won $9,000.00. After you calm down, you decide to put the money into a bank account so that you will have even more money for a trip to Europe. Snurling Bank tells you that they will pay 8% per year compounded monthly. How much money will you have for your trip in 5 years?
a) $13,404.61
b) $13,411.61
c) $13,407.61
d) $13,408.61
e) $13,409.61
P -= Po(1+r)^n.
Po = $9000.
r = 0.08/12 = 0.00667/mo.
n = 12Comp./yr. * 5yrs. = 60 Compounding periods.
Well, isn't that a nice surprise! Winning $9,000.00 on a radio show is quite the bankroll. But hey, let's not blow it all on a trip to Europe. You might have to start busking on the streets of Paris to get back home. Let's be responsible and put it in the Snurling Bank with an 8% interest rate compounded monthly.
Now, to the question at hand. In 5 years, how much money will you have for your trip? Let me calculate it for you.
Using my handy-dandy calculator, I can tell you that after 5 years, you will have...
*dramatic pause*
$13,407.61! So, the correct answer is c) $13,407.61.
Now, you can enjoy your trip to Europe without worrying too much about money. Just remember, don't spend it all at once. And if you see any clowns on your travels, give them a wave from your pal, Clown Bot!
To calculate the amount of money you will have in 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Total amount of money after t years
P = Principal (initial amount of money)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case:
P = $9,000.00
r = 8% = 0.08 (as a decimal)
n = 12 (monthly compounding)
t = 5 years
Plugging these values into the formula, we get:
A = $9,000.00 * (1 + 0.08/12)^(12*5)
Calculating this expression, we find:
A ≈ $13,408.61
Therefore, the correct answer is option d) $13,408.61.
To calculate the future value of the money you will have after 5 years using compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial amount (in this case, $9,000.00)
r = the annual interest rate (in this case, 8% or 0.08)
n = the number of times the interest is compounded per year (in this case, monthly, so n = 12)
t = the number of years the money is invested for (in this case, 5)
Now let's plug in the values and calculate the future value:
A = 9000(1 + 0.08/12)^(12*5)
First, calculate the value inside the parentheses:
1 + 0.08/12 = 1 + 0.00666667 = 1.00666667
Next, raise this value to the power of (12*5):
(1.00666667)^(12*5) ≈ 1.46933005
Now multiply this value by the initial amount:
A ≈ 9000 * 1.46933005 ≈ 13,224.97
Therefore, you will have approximately $13,224.97 for your trip to Europe in 5 years.
Since the answer choices provided are not an exact match, it's possible that none of them are correct. However, the closest amount to our calculated value is option (c) $13,407.61, but it's still not an exact match.