How much money would a person need to deposit today at 9% annual interest compounded monthly to have 12000. in the account after 6 Years?
PV = 12000(1 + .09/12)^-72
= 12000(1.0075)^-72
= $7007.08
Thank you very much. I just needed the formula and you provided that so now I understand to resolve these type of problems
To calculate the amount of money needed to deposit today, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A is the future value of the account (12000),
P is the principal amount (the initial deposit we are trying to find),
r is the annual interest rate (9% in this case),
n is the number of times the interest is compounded per year (monthly compounding, so n = 12),
and t is the number of years (6).
First, we need to rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Plugging in the provided values:
P = 12000 / (1 + 0.09/12)^(12*6)
Now, let's solve it step-by-step:
P = 12000 / (1 + 0.0075)^(72)
P = 12000 / (1.0075)^(72)
P = 12000 / 1.68900422
P ≈ 7105.94
Therefore, a person would need to deposit approximately $7,105.94 today to have $12,000 in the account after 6 years at an annual interest rate of 9%, compounded monthly.
To calculate the amount of money a person would need to deposit today at 9% annual interest compounded monthly to have $12,000 in the account after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (in this case, $12,000)
P = the principal (the initial deposit we are trying to calculate)
r = the annual interest rate (9% or 0.09 in decimal form)
n = the number of times interest is compounded per year (12 for monthly compounding)
t = the number of years (6 in this case)
Now, let's rearrange the formula to solve for P (the principal):
P = A / (1 + r/n)^(nt)
Substituting the given values:
P = $12,000 / (1 + 0.09/12)^(12*6)
P = $12,000 / (1 + 0.0075)^(72)
P = $12,000 / (1.0075)^(72)
Now, using a calculator or spreadsheet, calculate (1.0075) raised to the power of 72, and divide $12,000 by this result to find P:
P ≈ $6,454.38
Therefore, a person would need to deposit approximately $6,454.38 today at 9% annual interest compounded monthly to have $12,000 in the account after 6 years.