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Zola buys annuity that pays R4000 a year for the next 20 years. The expect annul interest rates will be 8% over that time period. The maximum price she will pay for the annuity is _?
Anonymous
more than 4 weeks ago
Zola buys annuity that pays R4000 a year for the next 20 years. The expect annul interest rates will be 8% over that time period. The maximum price she will pay for the annuity is _?
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more than 4 weeks ago
To calculate the maximum price Zola should pay for the annuity, we need to find the present value of the annuity payments.
The formula to calculate the present value of an annuity is:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value
PMT = Payment per period (R4000)
r = Interest rate per period (8% or 0.08)
n = Number of periods (20 years)
Plugging in the values:
PV = R4000 * [(1 - (1 + 0.08)^-20) / 0.08]
PV = R4000 * [(1 - (1.08)^-20) / 0.08]
PV = R4000 * [(1 - 0.21455) / 0.08]
PV = R4000 * [0.78545 / 0.08]
PV = R4000 * 9.818125
PV = R39,272.50
Therefore, the maximum price Zola should pay for the annuity is R39,272.50.
The formula to calculate the present value of an annuity is:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value
PMT = Payment per period (R4000)
r = Interest rate per period (8% or 0.08)
n = Number of periods (20 years)
Plugging in the values:
PV = R4000 * [(1 - (1 + 0.08)^-20) / 0.08]
PV = R4000 * [(1 - (1.08)^-20) / 0.08]
PV = R4000 * [(1 - 0.21455) / 0.08]
PV = R4000 * [0.78545 / 0.08]
PV = R4000 * 9.818125
PV = R39,272.50
Therefore, the maximum price Zola should pay for the annuity is R39,272.50.
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