Question

In: Finance

Find the PV of a 15-year annuity-immediate with payments of 15, 14, 13, ..., 1 at...

Find the PV of a 15-year annuity-immediate with payments of 15, 14, 13, ..., 1 at an annual effective rate of interest
i = 3%.

Find the PV of a 26-year annuity-immediate with payments of 1, 2, 3, ..., 26 at an annual effective rate of interest
i= 7%.

Solutions

Expert Solution

Number of years =15
Rate =3%
PV of annuity due =15+14/1.03+13/1.03^2+12/1.03^3+11/1.03^4+10/1.03^5+9/1.03^6+8/1.03^7+7/1.03^8+6/1.03^9+5/1.03^10+4/1.03^11+3/1.03^12+2/1.03^13+1/1.03^14=105.13

PV of 26 year annuity due =1+2/(1+7%)+3/(1+7%)^2+4/(1+7%)^3+5/(1+7%)^4+6/(1+7%)^5+7/(1+7%)^6+8/(1+7%)^7+9/(1+7%)^8+10/(1+7%)^9+11/(1+7%)^10+12/(1+7%)^11+13/(1+7%)^12+14/(1+7%)^13+15/(1+7%)^14+16/(1+7%)^15+17/(1+7%)^16+18/(1+7%)^17+19/(1+7%)^18+20/(1+7%)^19+21/(1+7%)^20+22/(1+7%)^21+23/(1+7%)^22+24/(1+7%)^23+25/(1+7%)^24+26/(1+7%)^25 =124.98


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