Bob and Barbara are friends. Bob takes out a 10,000 loan and agrees to repay it
ID: 2720114 • Letter: B
Question
Bob and Barbara are friends. Bob takes out a 10,000 loan and agrees to repay it over twelve years by making annual level payments at an effective rate of 5.62499%. At the same time, Barbara takes out a 10,000 loan and agrees to repay it by making annual interest payments at an annual effective interest rate of i. She also agrees to make annual level deposits into a sinking fund that earns 4% annual effective interest so as to accumulate 10,000 at the end of the twelve years. Bob and Barbara discover they have the same total annual expenditures resulting from their loans. Find the rate i. SHOW WORK PLEASE ANSWER IF YOU GET AROUND THIS ANSWER OR EXACT ANSWER IN BACK OF BOOK: 5.0285%
Explanation / Answer
Annual Payment of Bob = pmt(rate,nper,,pv,fv)
Annual Payment of Bob = pmt(5.62499%,12,-10000,0)
Annual Payment of Bob = $ 1168.37
Barbara
Annual Deposit in sinking Fund = pmt(rate,nper,pv,fv)
Annual Deposit in sinking Fund = pmt(4%,12,0,10000)
Annual Deposit in sinking Fund = $ 665.52
Total annual expenditures is same for both freind
Annual Interest Payment of Barbara = Annual Payment of Bob- Annual Deposit in sinking Fund
Annual Interest Payment of Barbara = 1168.37-665.52
Annual Interest Payment of Barbara = $ 502.85
Rate of i = Annual Interest Payment of Barbara/Loan Amount
Rate of i = 502.85/10000
Rate of i =5.0285%
Answer
Rate of i =5.0285%