Phillip and Kayla have just had a baby girf named Nicky. They want to give Nicky R 230000 on her \( 21^{\text {It }} \) birthday for her university tuition. How much do they need to invest today, if the account earns \( 9,3 \% \) compound interest per year?

To determine how much Phillip and Kayla need to invest today, we can use the formula for present value of a future sum of money: \[ PV = \frac{FV}{(1 + r)^n} \] where \( PV \) is the present value (the amount to invest today), \( FV \) is the future value (R 230,000), \( r \) is the annual interest rate (9.3% or 0.093), and \( n \) is the number of years until Nicky turns 21 (which is 21 years). Plugging in the values: \[ PV = \frac{230000}{(1 + 0.093)^{21}} \] \[ PV = \frac{230000}{(1.093)^{21}} \] \[ PV = \frac{230000}{6.376} \] \[ PV \approx R 36,160.63 \] So, Phillip and Kayla need to invest approximately R 36,160.63 today to have R 230,000 for Nicky’s university tuition on her 21st birthday. To kick it up a notch, think of "time travel" in finance! Money has the magical ability to grow over time. The earlier you invest, the more it can snowball thanks to compounding interest. Just like nurturing a small seed into a mighty tree, your diligent investment can flourish into a hefty amount over the years. So why not start early and let those compounding powers work in your favor! Did you know that the rule of 72 is a simple trick for estimating how long it will take for your investment to double? Just divide 72 by your expected annual rate of return. With a 9.3% interest, you can expect your money to double in about 7.74 years. This little rule can help you put your investment growth into perspective and keep you motivated along your financial journey!