Keep the Highest: 2 Attempts: 8. Implied interest rate and period Consider the c
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Keep the Highest: 2 Attempts: 8. Implied interest rate and period Consider the case of the following annuities, and the need to compute either their expected rate of return or Aa Aa duration Anthony inherited an annuity worth $5,288.17 from his uncle. The annuity will pay him six equal payments of $1,250 at the end of each year. The annuity fund is offering a return of Anthony's friend, Sachit, has hired a financial planner for advice on retirement. Considering Sachit's current expenses and expected future lifestyle changes, the financial planner has stated that once Sachit crosses a threshold of 10,918,096 in savings, he will have enough money for retirement. Sachit has nothing saved for his retirement yet, so he plans to start depositing $25,000 in a retirement fund at a fixed rate of 11.00% at the end of each year. It will take years for Sachit to reach his retirement goal. Flash Player WIN 30,0,0,154 3 3.34.1 2004-2016 Aplia. All rights reserved C 2013 Cengage Learning except as noted. All rights reserved. Grade It Now Save & ContinueExplanation / Answer
8. Implied Interest rate & period a..We need to find the interest rate at which the PV of the 6 annual year-end payments of $ 1250 will equal $ 5288.17 So, PV of the annuity= 5288.17 The annuity ie. PMT= 1250 r= ? (to be found out) n= no.of annuities=6 So, using the PV of ordinary annuity formula, PV=PMT.*(1-(1+r)^-n)/r Substituting the above values, 5288.17=1250*(1-(1+r)^-6)/r r= 11% The annuity fund is offering a return of 11% Verification : Year Annuity Interest at 11% Tow. Principal Principal bal. 0 5288.17 1 1250 581.70 668.30 4619.87 2 1250 508.19 741.81 3878.05 3 1250 426.59 823.41 3054.64 4 1250 336.01 913.99 2140.65 5 1250 235.47 1014.53 1126.12 6 1250 123.87 1126.13 0.00 Total 7500 2211.83 5288.17 b…Here, the Future Value (FV)of the $ 25000 year-end annuities =10918096 at 11% interest rate for n no.of yrs. Again, substituting the given values in the FV of year-end formula, FV = Pmt(.(1+r)^n-1)/r 10918096=25000*(1.11^n-1)/0.11 Solving for n, n= 37.3 years No.of yrs. For Sachit to reach his retrement goal will be roughly 37 years.
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