Question

answer is $9508.90 explain without excel

Gerry pays $W to buy a ten-year annuity with end-of-year payments of $1,400. This purchase price allows her to replace her capital by means of a savings account that has an annual effective interest rate of 3% and also to earn an overall annual yield of 6% for the ten years of the annuity. Find W.

Answer 1

Principal=W
Interest every year=W*6%
Amount needed every year to accumulate W in future=W*3%/(1.03^10-1)

Yearly interest=W*6%
Yearly principal=W*3%/(1.03^10-1)

Total yearly payment=Yearly interest+Yearly principal
=>1400=W*3%/(1.03^10-1)+W*6%
=>W=1400/(6%+3%/(1.03^10-1))
=>W=9508.90