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, 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
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 | ||||||