Financial Maths, STD2 EQ-Bank 29

Shown below is part of the output from a spreadsheet used to model a 25-year reducing balance loan with equal monthly repayments and a constant interest rate, $r$, expressed as a decimal.

Note that many rows and values have been removed from the output shown.

Show that the amount owing at the end of month 120 is $407 860.99. (4 marks)

--- 7 WORK AREA LINES (style=lined) ---

Show Answers Only

$\text{See worked solution}$

Show Worked Solution

$\text{Find } r:$

$\text{Interest}$	$= r \times \text{amount owing}$
$3500$	$= r \times 500\,000$
$r$	$= 0.007$

$\text{Find monthly repayment using PVIF table:}$

$\text{At } N = 300\ \text{ and }\ r = 0.007,\ \text{ PVIF} = 125.23492$

$\text{Monthly repayment}= \dfrac{500\,000}{125.23492}= \$3992.50$

$\text{Amount owing at start of month 120:}$

$\text{Amount owing at end of month 119} = \$408\,990.56$

$\therefore\ \text{Interest charged in month 120}$	$= 0.007 \times \$408\,990.56$
	$= \$2862.93$

$\text{Amount owing at end of month 120:}$

$= \$408\,990.56+\$2862.93-\$3992.50$

$= \$407\,860.99 \quad \checkmark$

\(\text{Interest}\)	\(= r \times \text{amount owing}\)
\(3500\)	\(= r \times 500\,000\)
\(r\)	\(= 0.007\)