Saving for Retirement

At the age of $30,$ Arash 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.

I$-$ 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, Arash 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?

Plan to achieve his vacation objective

Deposit $$150$ at the end of every month for ten years into a savings account that earns $3\%$ compounded monthly. At the end

of the ten years, transfer the accumulated money into an investment fund that earns $6\%$ compounded quarterly, and allow

the money to grow in this fund until retirement.

b$.$ How long $($in years and months$)$ would it take to accumulate the required amount of $$45,000$ to pay for his vacation?

c$.$ To ensure that the amount accumulates to only $$45,000$ at the time of retirement, by how much should he change his

monthly deposit?

Plan to achieve his monthly allowance objective

He will save $$500$ at the beginning of every month until retirement in an RRSP that has an interest rate of $5\mathrm{.}4\%$ compounded

monthly.

d$.$ What would be the accumulated value of the RRSP at the time of retirement?

e$.$ For Arash to be able to withdraw $$2000$ from the RRSP at the beginning of every month during his planned $20-$

year retirement period, what does the nominal interest rate, compounded monthly, need to change to$,$ assuming the

interest rate during the $25-$year savings period remains unchanged at $5\mathrm{.}4\%$ compounded monthly?