Question

Miguel wants to buy an entertainment system as a gift for his sister’s wedding. He estimates that when she marries 1 year from now, the system will cost $2499, plus GST (government sales tax) at 6% and PST (provincial sales tax) at 8%. He knows he can deposit $225 a month into an account earning 3.5%/a compounded monthly. Will he have enough money to buy the gift? Explain.

Answer 1

given that the gift cost = [ $2499 +( 6% GST + 8% PST) 0f $2499 ]

=$2499 + $2499 *(14%)= $2499 + $349.86 = $2848.86

thus total cost of gift is $2848.86

now, the monthly deposit in an account is $225, with rate 3.5% per annum i.e. rate = $\frac{3.5}{12}$ per month and the time is = 12 months.

The amount after one month will be --------

$amount=principle amount*(1+\frac{rate}{100})^{time}=225*(1+\frac{3.5}{1200})^{1}$

$amount=225*(\frac{1203.5}{1200})^{1}=225*(1.00291667)$

amount = $225.656

after second month the pinciple amount is 225 + 225.656 = $450.656

and the amount after compounded = $450.656*(1+\frac{3.5}{1200})^1$ = 451.971

3rd month principle amount = 451.971 + 225 = $676.971

amount after 3rd month = $676.971*(1+\frac{3.5}{1200})^1= 678.948$

similarly we can find month by month amount after compounded till 12 months.

amount after 4th month = $906.587

amount after 5th month = $1134.892

amount after 6th month = $1363.862

amount after 7th month = $1593.502

amount after 8th month = $1823.812

amount after 9th month = $2054.795

amount after 10th month = $2286.452

amount after 11th month = $2518.785

amount after 12th month = $2751.797

we can see that Miguel have amount of money less than the gift will be cost. Hence, Miguel can't buy the gift after one year.