Revision as of 14:39, 19 November 2023 by Admin (Created page with "A car dealership offers a 120-month loan for a blue car costing 30,000, with an annual nominal interest rate of 9% compounded monthly and level end-of-month payments. The dealership also offers a loan for a red car costing 33,000, with the same interest rate and end-of-month payments as for the loan for the blue car. Calculate the number of months needed to pay off the loan for the red car <ul class="mw-excansopts"><li>132</li><li>135</li><li>138</li><li>140</li><li>14...")
ABy Admin
Nov 19'23
Exercise
A car dealership offers a 120-month loan for a blue car costing 30,000, with an annual nominal interest rate of 9% compounded monthly and level end-of-month payments. The dealership also offers a loan for a red car costing 33,000, with the same interest rate and end-of-month payments as for the loan for the blue car.
Calculate the number of months needed to pay off the loan for the red car
- 132
- 135
- 138
- 140
- 141
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: E
[[math]]
\begin{aligned}
& 30,000=P a_{\overline{120} \mid 0.0075} \\
& P=380.03 \\
& 33,000=380.03 a_{\overline{n} |0.0075} \\
& n=141
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.