Final answer:
The lump sum that the insurance company must put into a bank account to ensure a payment of $42,000 per year at a 1.5% interest rate, assuming a perpetuity, is $2.8 million.
Step-by-step explanation:
Victor has a life insurance policy that will pay his family $42,000 per year if he dies. To answer this, we need to determine the present value of an annuity that provides $42,000 per year at an interest rate of 1.5%. The present value (PV) of an annuity formula is PV = Pmt * [(1 - (1 + r)^-n) / r], where Pmt is the annual payment, r is the interest rate, and n is the number of years. However, since the question does not specify the number of years (it could be for an indefinite period considering it's a life insurance payout), we assume a perpetuity.
For a perpetuity, the formula simplifies to PV = Pmt / r. So, the lump sum that the insurance company must put into a bank account is calculated as follows:
PV = $42,000 / 0.015.
PV = $2,800,000.
Therefore, the correct answer is b) $2.8 million.