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

Answer:

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.

Step-by-step 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

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

$P\:=\frac{A}{\left(1\:+\:\frac{r}{n}\right)^{nt}}$

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

$P\:=\frac{1000000}{\left(1\:+\:\frac{0.06}{12}\right)^{12\cdot 45}}\:$

    $=\frac{1000000}{1.005^{540}}$

$P = 67659.17$ $

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.