The interest rate is 4%. What is the PV of a 10-year ordinary annuity of 1,000 per year plus an additional 5,000 at the end of year 6?

The present value of a payment P, made after n years with the annual rate of interest r is equal to P/(1+r)^n.

The annuity in the problem consists of payments of $1000 at the end of 10 consecutive years, in addition to one payment of $5000 at the end of year 6.

The present value of this annuity is:

1000/(1.04) + 1000/(1.04)^2 +...(1000/(1+1.04)^10 + 5000/(1.04)^6

= 1000*(1/1.04+1/1.04^2 +...1/1.04^10) + 5000/(1.04)^6

= 1000*(1.04^10-1)/(1.04 - 1) + 5000/(1.04)^6

= 15957.68

The present value of the annuity is $14534.37

Comments

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