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Homework answers / question archive / Implied interest rate and period Consider the case of the following annuities, and the need to compute either their expected rate of return or duration Anthony needed money for some unexpected expenses, so he borrowed $3,289
Implied interest rate and period Consider the case of the following annuities, and the need to compute either their expected rate of return or duration Anthony needed money for some unexpected expenses, so he borrowed $3,289.13 from a friend and agreed to repay the loan in six equal installments of $300 at the end of each year. The agreement is offering an implied interest rate 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 $1,121.164 in savings, he will have enough money for retirement Sachit has nothing saved for his retirement yet, so he plans to start depositing $40,000 in a retirement fund at a fixed rate of 12.00% at the end of each year. It will take years for Sachit to reach his retirement goal.
Answer to Question 14:-
Part-A:-
Calculation of Intrest rate
Loan Amout =3,289.13
Installements =800 per year
Periods = 6
Installement = Loan Amount / [ 1 - [(1+r)^-n]] /r
800=3,289.13 / [ 1 - [(1+r)^-6]] /r
[ 1 - [(1+r)^-6]] /r = 3,289.13/ 800
[ 1 - [(1+r)^-6]] /r = 4.1114125
[ 1 - [(1+r)^-6]] = 4.1114125 * r
[(1+r)^-6] =1 - 4.1114125* r
r =12%
Therefore agreement offering implied rate of 12%p.a
Part-B:-
Calculatio of Period of Installement to reach retriement goals -
Cash Flows/Deposits = $ 40,000
FV of Retriemnt Goal = $ 1,121,164
Rate =12%
FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$1,121,164 =$40,000*[ [(1+0.12)^n ] - 1 ] /0.12
1,121,164 = 3,33,333 *[ [(1+0.12)^n ] - 1 ]
[ [(1+0.12)^n ] - 1 ] = 1,121,164/ 3,33,333
[ [(1+0.12)^n ] - 1 ] = 3.36
[(1+0.12)^n ] = 4.36
n=13 Years
Therefore, Period of Installement to reach retriement goals is 13 Years
