If a 10-year certain annuity with an installment refund is purchased and the annuitant dies after 5 years, how many payments remain?

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In the context of a 10-year certain annuity with an installment refund, if the annuitant dies after receiving payments for 5 years, we need to consider how the annuity structure operates.

This type of annuity guarantees that the annuitant will receive payments for a minimum of 10 years, regardless of whether they are alive for the entire duration. Since the annuitant has already received payments for 5 years, this means there are still 5 years of guaranteed payments left.

The payment frequency is typically monthly, which means there are 12 payments per year. Therefore, if there are 5 years remaining, the total number of payments that will be made is calculated by multiplying the remaining years by the number of payments per year:

5 years x 12 payments/year = 60 payments.

This reasoning demonstrates that even with the annuitant's passing, the remaining payments are guaranteed to be made to a beneficiary or the estate, totaling 60 payments to reach the end of the guaranteed period.