Grandma wants to make a single deposit so that she can cover her dental expenses for the next three years. She will need R 1000 at the end of year 1, R1 200 at the end of year 2 and R 1 500 at the end of year 3. She earns interest at 6% p.a., compounded annually. How much must grandma invest today to cover her expected future dental expenses?

Answer 1

To calculate how much Grandma must invest today to cover her dental expenses for the next three years, we can use the formula for compound interest:

A = P(1 + r)^n

Where:
A = the future amount needed (R 1 000 at the end of year 1, R 1 200 at the end of year 2, and R 1 500 at the end of year 3)
P = the principal amount (the amount Grandma needs to invest today)
r = the annual interest rate (6% or 0.06)
n = the number of years the money is invested for (3 years)

We can set up three equations for each year's amount needed:

Year 1:
1000 = P(1 + 0.06)^1
1000 = P(1.06)

Year 2:
1200 = P(1 + 0.06)^2
1200 = P(1.1236)

Year 3:
1500 = P(1 + 0.06)^3
1500 = P(1.191016)

Adding these equations together, we get:

1000 + 1200 + 1500 = P(1.06 + 1.1236 + 1.191016)
3700 = P(3.374616)

Solving for P, we get:

P = 3700 / 3.374616
P ≈ R 1096.25

Therefore, Grandma needs to invest approximately R 1096.25 today to cover her expected dental expenses for the next three years.