Question

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. With this annuity, what is April's monthly payment amount?

Answer 1

Explanation:

its 5628.18

Answer 2

Monthly payment is $5970

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,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

Discount factor
`D=(1-(1+i)^(-n))/(i)`

Where, Amount = $1,000,000

Rate r= 4.4%=0.044 compounded monthly

`i=(0.044)/(12)=0.004`

Time = 89-65=23 years

`n=23*12=276`

Now, put all the values we get,

`D=(1-(1+i)^(-n))/(i)`

`D=(1-(1+0.004)^(-276))/(0.004)`

`D=(1-(1.004)^(-276))/(0.004)`

`D=(1-0.33)/(0.004)`

`D=(0.67)/(0.004)`

`D=167.5`

Monthly payment,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

`M=(1000000)/(167.5)`

`M=5970.1`

Approximately,monthly payment is $5970