On retirement Victor was offered the option of receiving monthly payment of $1674.08 or a lump-sum payment of $150667
a) What are the respective incomes per annum of each option if the lump sum can be invested at 11.5% p.a.
b) At what interest rate must the lump sum be invested in order for the yearly interest to exceed the yearly superannuation payment?
To find the respective incomes per annum of each option, let's first calculate the annual income from the monthly payment option.
a) Income per annum from monthly payments:
Since Victor will receive $1674.08 per month, the annual income can be calculated by multiplying this amount by 12 (months in a year):
Annual Income = $1674.08 * 12 = $20,088.96
Now, let's calculate the income per annum from the lump-sum payment option, considering an annual interest rate of 11.5%:
Step 1: Calculate the interest earned on the lump sum investment:
Interest Earned = Lump Sum * Interest Rate = $150,667 * 0.115 = $17,329.05
Step 2: Add the interest earned to the original lump sum to calculate the total amount after one year:
Total Amount = Lump Sum + Interest Earned = $150,667 + $17,329.05 = $168,996.05
Therefore, the income per annum from the lump-sum payment option is $168,996.05.
b) To find the interest rate required for the yearly interest to exceed the yearly superannuation payment, we need to solve for the interest rate in the following equation:
Annual Interest > Superannuation Payment
Let's assume the interest rate required is "r" and solve for it:
Lump Sum * r > Monthly Payment * 12
Substituting in the given values:
$150,667 * r > $20,088.96
Simplifying the equation:
r > $20,088.96 / $150,667
r > 0.1333 (approximately)
Therefore, the interest rate must be greater than 13.33% (approximately) for the yearly interest to exceed the yearly superannuation payment.