Saving for Retirement

At the age of $30,$ Pippin decided to create a financial plan to retire in $25$ years. He had the

following retirement objectives:

$$ Home purchase objective: Own a home worth at least $$1,200,000$ with no mortgage.

$$ Vacation objective: Have an amount of $$45,000$ for a European tour.

$$ Retirement Monthly allowance objective: Receive a month$-$beginning allowance of

$$2000$ for $20$ years after retirement.

He created the following financial plans to achieve the above retirement objectives. Answer the

questions related to each plan.

Plan to achieve his home purchase objective

Assuming that the value of a property in a Toronto suburb would double over $25$ years, Pippin

would purchase a house worth $$600,000$ by making a down$-$payment of $$30,000$ and obtaining a

mortgage for the balance amount from a local bank at an interest rate of $4\%$ compounded semi$-$

annually for $25$ years.

a$)$ If the interest rate is constant over the $25-$year period, calculate the month$-$end payments

for the mortgage. What would be his total investment in the house over the term?