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

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

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$  

Where, Amount = $1,000,000

Rate r= 4.4%=0.044 compounded monthly

$i=\frac{0.044}{12}=0.004$  

Time = 89-65=23 years

$n=23\times12=276$  

Now, put all the values we get,  

$D=\frac{1-(1+i)^{-n}}{i}$  

$D=\frac{1-(1+0.004)^{-276}}{0.004}$  

$D=\frac{1-(1.004)^{-276}}{0.004}$  

$D=\frac{1-0.33}{0.004}$  

$D=\frac{0.67}{0.004}$  

$D=167.5$  

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

$M=\frac{1000000}{167.5}$  

$M=5970.1$  

Approximately,monthly payment is $5970

Answer 2

Answer:

The answer is $5628.18 for Apex.