Question

When you graduate college at the age of 20, you want to start saving up for retirement. If your investment pays a fixed APR of 9% and you want to have $2.5 million when you retire in 45 years, how much would you need to deposit, on a monthly basis, to reach this goal? Assume an ordinary annuity. a. $339.55 c. $337.62 b. $338.41 d. $336.21

Answer 1

its c.337.62

Explanation:

Answer 2

You need to deposit $337.62 each month, to reach this goal.

Solution-

We know that,

`\text{FV of annuity}=P[((1+r)^n-1)/(r)]`

Where,

P = periodic payment

r = rate per period

n = number of period

Here,

`FV\ of\ annuity=2,500,000,\\\\P=?,\\\\r = 9\%\ annually=(9)/(12)\%\ monthly=(9)/(1200)\ monthly\\\\n=45\ years=45* 12=540\ months`

Putting the values,

`\Rightarrow 2500000=P[\frac{(1+(9)/(1200))^(540)-1}{{(9)/(1200)}}]`

`\Rightarrow P=\frac{2500000}{[\frac{(1+(9)/(1200))^(540)-1}{{(9)/(1200)}}]}`

`\Rightarrow P=(2500000)/((56.5365-1)/(0.0075))`

`\Rightarrow P=(2500000)/((55.5365)/(0.0075))`

`\Rightarrow P=337.62`