Question

How much money should be deposited today in an account that earns 6% compounded monthly so that it will accumulate to $1000000 (one million dollars) in 45 years?

Answer 1

The principal investment required to get a total amount of $ 1,000,000.00 from compound interest at a rate of 6% per year compounded 12 times per year over 45 years is $ 67,659.17.

Explanation:

Given

• Accrued Amount A = $1000000

• Interest rate r = 6% = 0.06

• Time period t = 45 years

• Compounded monthly n = 12

To determine:

• Principle amount P = ?

Using the formula

`A\:=\:P\left(1\:+\:(r)/(n)\right)^(nt)`

`P\:=(A)/(\left(1\:+\:(r)/(n)\right)^(nt))`

substituting A = 1000000, r = 0.06, t = 45, and n = 12

`P\:=(1000000)/(\left(1\:+\:(0.06)/(12)\right)^(12\cdot 45))\:`

`=(1000000)/(1.005^(540))`

`P = 67659.17` $

Therefore, the principal investment required to get a total amount of $ 1,000,000.00 from compound interest at a rate of 6% per year compounded 12 times per year over 45 years is $ 67,659.17.