47. John wants to travel overseas in 5 years time. He has been told that he will need R50 000 to cover all his costs. How much should he invest now if his bank offers him an interest rate of \( 8 \% \) p.a. compounded annually?

To determine how much John should invest now, we can use the formula for present value, which is: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \(PV\) = Present Value (the amount to invest now) - \(FV\) = Future Value (the amount needed in the future, which is R50,000) - \(r\) = interest rate (8% or 0.08) - \(n\) = number of years until the future value is needed (5 years) Plugging in the numbers: \[ PV = \frac{50,000}{(1 + 0.08)^5} = \frac{50,000}{(1.469328)} \approx R34,045.10 \] So, John should invest approximately R34,045.10 now to ensure he has R50,000 in 5 years for his overseas trip! Investing today at a high interest rate, like 8%, really makes those future dreams more attainable! The earlier you start saving, the less you need to put away thanks to the power of compounding. Just think, if he didn't invest now, he'd miss out on all that potential growth—booo! It's like letting money just sit there, collecting dust instead of working hard for you!