After looking at the results of her calculations, Naomi has decided to aim for $500,000 savings by the time she retires. She expects to have a starting salary after college of $25,000 to $35,000 and she has taken into account all of the living expenses that will come out of her salary. What will Naomi's annual deposits need to be accumulate $500,000 in a CD at 6%?
You will have to tell me for how long she will make these annual deposits.
let's assume it is n years
so solve for P, the payment
500000 = P(1.06^n - 1)/.06
let me know what you got.
To calculate the annual deposits needed to accumulate $500,000 in a CD at 6%, we can use the formula for future value of a series of regular deposits. The formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = future value (desired savings of $500,000)
P = annual deposit
r = interest rate (6% or 0.06)
n = number of years
Rearranging the formula to solve for P:
P = FV * (r / [(1 + r)^n - 1])
In this case, FV = $500,000, r = 0.06, and we need to determine the value of n.
Since the question doesn't provide the number of years Naomi plans to save, we'll need to calculate it based on her starting salary. Let's assume that Naomi plans to save for n years.
To calculate the number of years needed to accumulate $500,000, we can rearrange the formula to solve for n:
n = log[(FV * r / P) + 1] / log(1 + r)
Now let's plug in the values and calculate the annual deposits and the number of years:
FV = $500,000
r = 0.06
P = annual deposit (to be determined)
n = log[(500,000 * 0.06 / P) + 1] / log(1 + 0.06)
Using these values, we can solve for P by trial and error or by using a financial calculator or spreadsheet software.
For example, let's try a starting salary of $30,000.
n = log[(500,000 * 0.06 / P) + 1] / log(1 + 0.06)
n = log[(30,000 * 0.06 / P) + 1] / log(1 + 0.06)
Assuming a financial calculator or spreadsheet software, try different values of P until the value of n results in a whole number or an acceptable decimal value.