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

Answer:

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

Step-by-step 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 × $(1+\frac{Rate}{12\times 100})^{12\times Time}$

$180,000 = P × $(1+\frac{6}{12\times 100})^{12\times 6}$

Or,  $180,000 = P × $(1.005)^{72}$

Or, $180,000 = P × 1.432

∴ P = $\frac{180,000}{1.432}$ = $125,698.324

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