Answer:
Monthly payment is $5970
Step-by-step explanation:
Given : April invested in a lifetime annuity that begins payments at age 65. Her life expectancy is 89. April invested a $1,000,000 into the annuity, which earns 4.4% APR compounded monthly.
To find : what is April's monthly payment amount?
Solution :
Formula of monthly payment
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Where, Amount = $1,000,000
Rate r= 4.4%=0.044 compounded monthly
[tex]i=\frac{0.044}{12}=0.004[/tex]
Time = 89-65=23 years
[tex]n=23\times12=276[/tex]
Now, put all the values we get,
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
[tex]D=\frac{1-(1+0.004)^{-276}}{0.004}[/tex]
[tex]D=\frac{1-(1.004)^{-276}}{0.004}[/tex]
[tex]D=\frac{1-0.33}{0.004}[/tex]
[tex]D=\frac{0.67}{0.004}[/tex]
[tex]D=167.5[/tex]
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
[tex]M=\frac{1000000}{167.5}[/tex]
[tex]M=5970.1[/tex]
Approximately,monthly payment is $5970
