Naledi Municipality estimates that it will need an amount of R 87 500 in eight years’ time and another R 44 000 in 11.2 years’ time to cover the expected maintenance on provincial roads. How much should they deposit today into an account that pays 12.5% interest per annum, compounded quarterly in order to cover the expected cost in eight and 11.2 years’ time respectively?
R 68 379.81
R 2 331.60
R 131 500.00
R 44 693.96
To calculate the amount that Naledi Municipality should deposit today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial deposit)
r = annual interest rate (decimal)
n = number of times that interest is compounded per year
t = number of years
First, let's calculate the amount needed in 8 years' time:
A1 = R 87 500
r = 0.125 (12.5%)
n = 4 (quarterly compounding)
t = 8 years
A1 = P(1 + 0.125/4)^(4*8)
87500 = P(1 + 0.125/4)^32
87500 = P(1.03125)^32
87500 = P(2.570489)
P = 87500/2.570489
P = R 34 043.96
Now, let's calculate the amount needed in 11.2 years' time:
A2 = R 44 000
r = 0.125
n = 4
t = 11.2 years
A2 = P(1 + 0.125/4)^(4*11.2)
44000 = P(1 + 0.125/4)^44.8
44000 = P(1.03125)^44.8
44000 = P(3.602266)
P = 44000/3.602266
P = R 12 235.85
Therefore, Naledi Municipality should deposit R 34 043.96 + R 12 235.85 = R 46 279.81 today in order to cover the expected maintenance costs in 8 and 11.2 years' time.