Question

To pay off an insurance settlement you must make monthly payments of $2500 for 6 years. How much should you invest in an account paying 6% compounded monthly to be sure you can make these payments over this time period?

Answer 1

The principal which should be invested in account is $125,698.324

Explanation:

Given as :

The monthly payment amount = $2500

The time period = 6 years = 6 × 12 = 72 months

So, The payment for 72 months = $2500 × 72 = $180,000

The rate of interest compounded monthly = 6%

The investment amount in account = P

Now, From compounded method

Amount = Principal ×
`(1+(Rate)/(12* 100))^(12* Time)`

$180,000 = P ×
`(1+(6)/(12* 100))^(12* 6)`

Or, $180,000 = P ×
`(1.005)^(72)`

Or, $180,000 = P × 1.432

∴ P =
`(180,000)/(1.432)` = $125,698.324

Hence The principal which should be invested in account is $125,698.324 . Answer