Case Study $-$ Retirement Planning

John is a $30-$year$-$old professional planning for his retirement. He wants to assess the financial impact of different

investment scenarios. He's considering investing a lump sum amount and wants to compare two options:

Option A: Invest R$50,000$ today for $30$ years.

Option B: Invest R$5,000$ per year for $30$ years.

Required:

$4\mathrm{.}1$ John's expected annual interest rate is $6\%.$ Help John evaluate both investment options using present

value $($PV$)$ and future value $($FV$)$ calculations. Calculate and compare the following for each option:

$$ The Future Value $($FV$)$ of the investment at the end of $30$ years.

$$ The Present Value $($PV$)$ of the investment $($if applicable$).$

$(18$ Marks$)$

$4\mathrm{.}2$ You plan to buy a house worth R$500,000,$ and you currently have R$100,000$ saved for this goal. If you can

invest your savings at an annual interest rate of $6\%,$ how long will it take for your savings to grow to the

required R$500,000$ for purchasing the house?