Question

In: Accounting

If an insurance company offers you annuity payments of $45,000 per year for the first 12 years of retirement and $52,000 per year for the next 12 years

If an insurance company offers you annuity payments of $45,000 per year for the first 12 years of retirement and $52,000 per year for the next 12 years, what would you be willing to pay for this annuity if you have a required rate of return of 6%? Assume beginning of year payments

Solutions

Expert Solution

The question is based upon time value of money.
Step-1:Present value of annuity for 12 years
Present value = Annuity * Present value of annuity of 1
= $     45,000.00 * 8.886874577
= $ 3,99,909.36
Working:
Present value of annuity of 1 = ((1-(1+i)^-n)/i)*(1+i) Where,
= ((1-(1+0.06)^-12)/0.06)*(1+0.06) i 6%
= 8.886874577 n 12
Step-2:Present value of annuity for next 12 years
Present value = Annuity * Present value of annuity of 1*Present value of 1
= $     52,000.00 * 8.886874577 * 0.496969
= $ 2,29,658.23
Working:
Present value 1 = (1+0.06)^-12 Where,
= 0.496969364 i 6%
n 12
Step-3:Value of annuity
Value of annuity is the present value of future annuity payments.
So, Value of annuity = $ 3,99,909.36 + $ 2,29,658.23
= $ 6,29,567.58

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