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Because you were born in 1938 - your full retirement age is 65 and 2 months.Assuming you start your social security benefits at your FRA - that are your full benefits without any reduction.Your wife's benefits are 79.2% of her full benefits because she started at 62.As she receives reduced benefits $13,000 - her full benefits are $16414.Thus if she were passing away before you - you will be entitled to the larger of surviving spouse benefits $16414 OR your own benefits $26,000 - whatever is larger.If you would pass away before her - similarly she will be entitled to the larger of surviving spouse benefits $26,000 OR your own benefits $16414 - whatever is larger - but either will be reduced to 79.2% because she started before her FRA.
As her surviving spouse benefits are larger - she would expect $26,000 * 79.2% = $20,592
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