Dream Car

Similar solution to that of Aaditya Bhatt , perhaps with more mathematics.

Future price $FV_{car}$ of your dream car based on its present price $PV_{car}$ in $n = 5$ years' time due to inflation:

$FV_{car} = PV_{car}(1+r_{inflation})^n = \$78,000(1+7.25\%)^5 = \$110,683.05$

The future value of your current $\$42,000$ deposit in bank due to interest rate $i$ :

$FV_{deposit} = PV_{deposit}(1+i)^n = \$42,000(1+9\%)^5 = \$64,622.21$

Extra amount of money in the future needed to buy your dream car:

$A_{extra} = FV_{car} - FV_{deposit} = \$46,060.84$

This amount must be paid by the $5$ annual installments $A$ also called annuity in the bank. That is:

$\begin{aligned} A_{extra} & = A_{annuity} \\ & = A(1+i) + A(1+i)^2+A(1+i)^3+...+A(1+i )^n \\ & = A \dfrac {(1+i)^n-1}{i} (1+i)\\ \Rightarrow \$46,060.84 & = \dfrac {1.09^5-1}{0.09} \times 1.09 A \\ \$46,060.84 & = 6.5233 A \\ \Rightarrow A & = \boxed{7,060.93} \end{aligned}$

You first have to find value of car after 5 years.

Inflation will increase price of car at = (1+0.0725)^5 * 78,000 = 1.4190*78,000 = $ 1,10,682.

Now your fixed deposit will grow at 9% and after 5 years it will be = (1+0.09)^5 * 42,000 = 1.5386 * 42,000 = $ 64,621.

So now after 5 years you must have additional $ 46,061 (1,10,682-64,621).

It says that you have to invest annually starting from today.

So apply annuity formula.

$\$46,061=Annuity\left( \frac { (1+0.09)^{ 5 }-1 }{ 0.09 } \right) *(1+0.09)$

Answer will be $7,061.