Wilma deposited a lump sum into a new bank account which earns 2% per annum compound interest - HSC - SSCE Mathematics Standard - Question 37 - 2020 - Paper 1
Question 37
Wilma deposited a lump sum into a new bank account which earns 2% per annum compound interest.
Present value interest factors for an annuity of $1 for various inter... show full transcript
Worked Solution & Example Answer:Wilma deposited a lump sum into a new bank account which earns 2% per annum compound interest - HSC - SSCE Mathematics Standard - Question 37 - 2020 - Paper 1
Step 1
Present value of $1000 annuity for 20 years
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Answer
To calculate the present value of an annuity of $1000 for 20 years at a 2% interest rate, we use the present value interest factor from the table:
Using the table, for 20 years at 2% interest rate, the present value interest factor is 16.351.
Thus, we compute:
PV=1000imes16.351=16,351
Step 2
Present value of $3000 annuity for 30 years
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Answer
Now, to find the present value of the withdrawals of $3000 for 30 years, we again refer to the table:
For 30 years at 2% interest rate, the present value interest factor is 22.396.
Thus the calculation becomes:
PV=3000imes22.396=67,188
Step 3
Present value of $3000 annuity for 20 years
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Answer
The next step is to find the present value of the withdrawals of $3000 for 20 years, starting 21 years from account opening:
Here, the present value interest factor for 20 years at 2% interest is still 16.351, but this presentation needs to account for the time shift:
The present value will be adjusted as:
PV=3000imes16.351=49,053
Step 4
Total present value calculation
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Answer
Finally, we sum all present values to find out how much Wilma needs to deposit originally:
TotalPV=16,351+67,188−49,053=34,486
Thus, the minimum lump sum Wilma must have deposited when she opened the new account is $34,486.
