Bill deposits $100 at the end of each year for 13 years into fund A. Seth deposi

Question

Bill deposits $100 at the end of each year for 13 years into fund A. Seth deposits $100 at the end of each year for 13 years into fund B. Fund A earns an annual effective rate of 15% for the first 5 years and 6% thereafter. Fund B earns an annual effective rate of i throughout the 13 years. The two funds have equal accumulated values at the end of 13 years. Find i.

The answer is 7.38007%, please show me how to do this.

Also, please dont give me the chegg answer by MiniatureEel4222, it doesnt yield the right answer when I solve for i.

Thank you

Explanation / Answer

Accumulated value of Fund A = 100*1.15^12 +100*1.15^11 +100*1.15^10 +100*1.15^9 +100*1.15^8 +100*1.15^7 +100*1.06^6 +100*1.06^5 +100*1.06^4 +100*1.06^3 +100*1.06^2 +100*1.06^1 +100*1.06^0 =$3167.90

Accumulated value of Fund B = 100*(1+i)^12 +100*(1+i)^11 +100*(1+i)^10 ...................100*(1+i)^0

100*(1+i)^12 +100*(1+i)^11 +100*(1+i)^10 ...................100*(1+i)^0 =3167.90

i= 13.81%

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