How much money would you need to deposit today at 9% annual interestcompounded monthly to have $12000 in the account after 6 years?
Question
How much money would you need to deposit today at 9% annual interestcompounded monthly to have $12000 in the account after 6 years?
Solution
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
We need to rearrange the formula to solve for P, the initial deposit:
P = A / (1 + r/n)^(nt)
We know that A = $12000, r = 9% or 0.09 (in decimal), n = 12 (since the interest is compounded monthly), and t = 6 years.
Substituting these values into the formula gives:
P = 12000 / (1 + 0.09/12)^(12*6)
Now, calculate the value inside the brackets:
= 12000 / (1 + 0.0075)^(72)
= 12000 / (1.0075)^(72)
Now, calculate the exponent:
= 12000 / 1.7138
Finally, divide 12000 by 1.7138 to find P:
P = $7000.37
So, you would need to deposit approximately 12000 in the account after 6 years with an annual interest rate of 9% compounded monthly.
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