Question

fv= 800(1.015)^12 - 1/0.015 (with a partial x4 on the left and a l above the bracket, likely a typo or partial writing)

Explanation:

Step1: Calculate the exponent part

First, we need to calculate \((1.015)^{12}\). Using a calculator, \((1.015)^{12}\approx1.195618\).

Step2: Subtract 1 from the result

Subtract 1 from the above result: \(1.195618 - 1 = 0.195618\).

Step3: Divide by 0.015 (assuming a typo, as 0.045 might be incorrect, likely 0.015 for monthly rate with annual rate 18%? Wait, original denominator is 0.015? Wait the formula seems like future value of an annuity: \(FV = P\times\frac{(1 + r)^{n}- 1}{r}\), here \(P = 800\), \(r = 0.015\), \(n = 12\). So denominator should be 0.015. Let's proceed with denominator 0.015 (maybe a writing error 0.045). So divide 0.195618 by 0.015: \(\frac{0.195618}{0.015}\approx13.0412\).

Step4: Multiply by 800

Multiply the result by 800: \(800\times13.0412 = 10432.96\). Wait, if denominator is 0.045 (maybe annual rate 4.5% with monthly compounding, but then \(r\) per month is 0.045/12 = 0.00375, but original formula has 1.015, so 1.015 is 1.5% per month, so annual rate 18%, monthly rate 1.5% = 0.015. So denominator should be 0.015. Let's recalculate with denominator 0.015:

\((1.015)^{12}=e^{12\ln(1.015)}\approx e^{12\times0.0148886}\approx e^{0.178663}\approx1.1956\)

\((1.015)^{12}-1 = 0.1956\)

\(\frac{0.1956}{0.015}=13.04\)

\(800\times13.04 = 10432\) (approx). If denominator is 0.045, then \(\frac{0.1956}{0.045}\approx4.3467\), \(800\times4.3467\approx3477.36\). But likely a typo, the correct denominator for monthly rate 1.5% (0.015) is 0.015. So assuming denominator is 0.015 (correct for \(r = 0.015\)):

Step1: Calculate \((1.015)^{12}\)

Using calculator, \((1.015)^{12}=\prod_{k = 1}^{12}(1.015)\approx1.195618171\)

Step2: Subtract 1

\(1.195618171 - 1 = 0.195618171\)

Step3: Divide by 0.015

\(\frac{0.195618171}{0.015}=13.0412114\)

Step4: Multiply by 800

\(800\times13.0412114 = 10432.96912\)

Answer:

\(\approx10433\) (if denominator is 0.015) or \(\approx3477\) (if denominator is 0.045, but likely denominator is 0.015, so 10433)