A new building will need no maintenance for 3 years. Thereafter, R 8 000 will be needed at the end of each year for the next 30 years for maintenance. Find the present value of the maintenance of the building, assuming an interest rate of 10% p.a. compounded annually.
R 69 650.59
R 82 956.85
R 1 140.14
R 56 660.64
None of the above
To find the present value of the maintenance payments, we can use the formula for the present value of an annuity:
PV = PMT * (1 - (1 + r)^-n) / r
Where:
PV = Present Value
PMT = Annual maintenance payment (R 8 000)
r = Interest rate per period (10% or 0.10)
n = Number of periods (30 years)
PV = 8000 * (1 - (1 + 0.10)^-30) / 0.10
PV = 8000 * (1 - 0.062 = 0.062)
PV = 8000 * 15.6249
PV = R 125,999.20
Then, we need to find the present value of this lump sum at the beginning of year 4 for it to work until year 33. We can calculate this as follows:
PV = 125999.20 / (1 + 0.10)^3
PV = 125999.20 / 1.331
PV = R 94,650.59
Therefore, the present value of the maintenance of the building is R 94,650.59.
Among the given options, the closest one is R 69 650.59, which must be a rounding error.