Answer: $11,044.79
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Step-by-step explanation:
We use this formula for compound interest
A = P*(1 + r/n)^(n*t)
The variables are,
- A = final amount after t years
- P = initial deposit aka principal
- r = annual interest rate in decimal form
- n = number of times we compound the money
- t = number of years
For the first year, we have this set of values
- P = 10,000
- r = 0.045
- n = 4
- t = 1
Which leads to this
A = P*(1 + r/n)^(n*t)
A = 10,000*(1 + 0.045/4)^(4*1)
A = 10,457.6508633057 approximately
A = 10,457.65 after rounding to the nearest cent
This value of A will be the new deposit value P when we do another round of calculations. For the second round, we have
- P = 10,457.65
- r = 0.055
- n = 4
- t = 1
So,
A = P*(1 + r/n)^(n*t)
A = 10,457.65*(1 + 0.055/4)^(4*1)
A = 11,044.7927637434
A = 11,044.79
There is $11,044.79 in the account after 2 years.
For each case, the value of n = 4 stays the same (since both rounds are compounding quarterly, aka 4 times a year). Also, we have t = 1 the same because each timespan is 1 full year.
Side note: The total amount of interest earned is 11,044.79 - 10,000 = 1,044.79 dollars.