What annual deposit would you need to make, beginning in one year, into an account paying 7% per year, compounded annually, in order to have $50,000 in it after 20 years, assuming that the account has nothing in it today?
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A. B. C. D. E.B
On the BAII Plus, press 20 N, 7 I/Y, 0 PV, 50000 FV, CPT PMT. On the HP12C, press 20 n, 7 i, 0 PV, 50000 FV, PMT. Note that the answer will be displayed as a negative number.
To calculate the annual deposit needed to accumulate $50,000 in an account after 20 years, we can use the formula for the future value of a series of regular deposits:
FV = P * ((1 + r)^n - 1) / r
Where: FV = Future value (target amount) P = Annual deposit r = Interest rate per period n = Number of periods
In this case, we want to find the annual deposit (P), given that: FV = $50,000 r = 7% or 0.07 (converted to decimal) n = 20
Let's substitute these values into the formula and solve for P:
$50,000 = P * ((1 + 0.07)^20 - 1) / 0.07
To simplify the calculation, we can use a financial calculator or a spreadsheet software like Excel. However, if you prefer to solve it step-by-step manually, we can break down the calculation:
Step 1: Calculate the term within the parentheses: (1 + 0.07)^20 - 1 ≈ 2.65329794
Step 2: Rearrange the formula to solve for P: $50,000 = P * 2.65329794 / 0.07
Step 3: Solve for P: P ≈ $50,000 * 0.07 / 2.65329794 ≈ $1,316.25
Therefore, the annual deposit needed to accumulate $50,000 in the account after 20 years is approximately $1,316.25.
Now, let's compare this result to the answer choices provided:
A. $1,129.56: Not the correct answer. B. $1,219.65: Not the correct answer. C. $4,719.65: Not the correct answer. D. $1,291.56: Not the correct answer. E. $2,191.65: Not the correct answer.
None of the given answer choices match the calculated value of approximately $1,316.25, so none of the options provided are correct.