What annual interest rate, compounded annually, would cause a series of 10 deposits of $1,000 to accumulate to $18,000, if the first deposit is made one year from today?
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A. B. C. D. E.B
On the BAII Plus, press 10 N, 0 PV, 1000 PMT, 18000 +/- FV, CPT I/Y. On the HP12C, press 10 n, 0 PV, 1000 PMT, 18000 CHS FV, i. Make sure that the BAII
Plus has the P/Y value set to 1.
To solve this problem, we can use the formula for the future value of an annuity:
FV = P * [(1 + r)^n - 1] / r
Where: FV = Future value of the annuity P = Periodic payment amount r = Annual interest rate n = Number of periods
In this case, we have 10 deposits of $1,000, so P = $1,000 and n = 10. We need to find the annual interest rate (r) that will result in a future value (FV) of $18,000.
Let's plug in the values into the formula and solve for r:
$18,000 = $1,000 * [(1 + r)^10 - 1] / r
To solve this equation, we can use trial and error or a financial calculator. However, since we have answer choices available, we can simply test each option to see which one satisfies the equation.
Let's start by testing option A: 14.49%. Plugging in r = 0.1449 into the formula:
$18,000 = $1,000 * [(1 + 0.1449)^10 - 1] / 0.1449
Evaluating the right side of the equation:
$18,000 = $1,000 * [(1.1449)^10 - 1] / 0.1449 $18,000 = $1,000 * [2.7135 - 1] / 0.1449 $18,000 = $1,000 * 1.7135 / 0.1449 $18,000 = $17,135.40
Option A does not give us the desired result. Let's move on to option B: 12.52%.
$18,000 = $1,000 * [(1 + 0.1252)^10 - 1] / 0.1252 $18,000 = $1,000 * [2.829 - 1] / 0.1252 $18,000 = $1,000 * 1.829 / 0.1252 $18,000 = $14,583.47
Option B also does not give us the desired result. Let's move on to option C: 12.69%.
$18,000 = $1,000 * [(1 + 0.1269)^10 - 1] / 0.1269 $18,000 = $1,000 * [2.867 - 1] / 0.1269 $18,000 = $1,000 * 1.867 / 0.1269 $18,000 = $14,706.78
Option C does not give us the desired result either. Let's try option D: 11.84%.
$18,000 = $1,000 * [(1 + 0.1184)^10 - 1] / 0.1184 $18,000 = $1,000 * [2.597 - 1] / 0.1184 $18,000 = $1,000 * 1.597 / 0.1184 $18,000 = $13,502.68
Option D also does not give us the desired result. Finally, let's try option E: 35.82%.
$18,000 = $1,000 * [(1 + 0.3582)^10 - 1] / 0.3582 $18,000 = $1,000 * [6.119 - 1] /