Suppose you have $600 to invest in a savings plan.Find the balance after one year if you deposit all the money into an account that pays 5% APR with monthly compounding.(Round to the nearest cent.)
Question
Suppose you have $600 to invest in a savings plan.Find the balance after one year if you deposit all the money into an account that pays 5% APR with monthly compounding.(Round to the nearest cent.)
Solution 1
To solve this problem, we need to use the formula for compound interest, which is:
A = P (1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
Given in the problem: P = $600 r = 5% or 0.05 (in decimal) n = 12 (since it's compounded monthly) t = 1 year
Substitute these values into the formula:
A = 600 (1 + 0.05/12)^(12*1)
Now, calculate the value inside the parenthesis:
= 600 (1 + 0.00416667) = 600 (1.00416667)
Then, raise this value to the power of 12:
= 600 (1.0512)
Finally, multiply by the principal amount:
A = $630.72
So, the balance after one year would be approximately $630.72.
Solution 2
To solve this problem, we need to use the formula for compound interest, which is:
A = P (1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
Given in the problem: P = $600 r = 5% or 0.05 (in decimal) n = 12 (since it's compounded monthly) t = 1 year
Substitute these values into the formula:
A = 600 (1 + 0.05/12)^(12*1)
Now, calculate the value inside the parenthesis:
A = 600 (1 + 0.00416667)
A = 600 (1.00416667)
Now, raise 1.00416667 to the power of 12:
A = 600 (1.0512)
Finally, multiply 600 by 1.0512 to get the total amount after one year:
A = $630.72
So, the balance after one year would be approximately $630.72 when rounded to the nearest cent.
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