Question

Mr. and Mrs. Corey are newlyweds and want to purchase a home, but they need a down payment of 30000 dollars. If they want to buy their home in 3 years, how much should they save each month in their savings account that pays 6% per annum compounded monthly?

Answer 1

\[1 st Month = P \]
\[2nd Month = P(1+R) + P \]
\[\text{3rd Month -$\quad $(P(1+R)+P)(1+R)+P= }

P + P (1 + R) + P (1 + R){}^{\wedge}2\]\[=P\left(1+(1+R)+(1+R)^2\right.

)\]

\[\text{4th Month$\quad $- }

P \left(1 + (1 + R) + (1 + R){}^{\wedge}2+(1+R)^3\right.

)\]
\[\text{Nth Month$\quad $- $\quad $}

P\left( 1+ (1 + R) + (1 + R){}^{\wedge}2 + (1 + R){}^{\wedge}3+\text{...}\text{..}+(1+R)^{N-1}\right.

)\]
\[\frac{1 - (1 + R)^N}{1-(1+R)}

=

\frac{1-(1+R)^N}{-R}\]
\[\text{ = P(}

\frac{1-(1+R)^N}{-R}

)\]

Answer 2

\[30000=P\frac{1-\left(1+\frac{.06}{12}\right)^{36}}{-\frac{.06}{12}}\]

Answer 3

P=762.66