Question

You put aside $300 a month in an account that returns 9% a year, compounded monthly. How long do you need to contribute to save $1,000,000

Answer 1

Answer:

36 years 4 months and 2 days

Explanation:

Data provided in the question:

Monthly payment = $300

Rate of return, i = 9% = 0.09

Future value = $1,000,000

Now,

we know

Future value = Monthly payments × $\left[ \frac{(1+i)^{n}-1}{i} \right]$

or

1000000  = $300 × $\left[ \frac{(1+0.0075)^{ }-1}{ 0.0075 }$

or

$\frac{ 1000000}{ 300} &= \frac{ 1.0075^{n} - 1}{ 0.0075}$

$3333.33333 &= \frac{ 1.0075^{n} - 1}{ 0.0075}$

$1.0075^{n} - 1 &= 3333.33333 \times0.0075$

or

1.0075ⁿ - 1 = 25

or

1.0075ⁿ = 26

ln( 1.0075ⁿ) = ln(26)

or

n × ln( 1.0075 ) = ln(26)

or

n = [tex]\frac{ \ln (26) }{ \ln( 1.0075 ) }[tex]

or

n = 436.04  months

or

n = 36 years 4 months and 2 days

Answer 2

Answer:

436 months or 36.33 years

Explanation:

monthly principal P = $300

Amount to be obtained A = $1,000,000

ROI per annum R% = 9%

or ROI per month r% = 9/12 = 0.75%

and n = no. of months

We know that

$A= P(1+\frac{r}{100})^n$

plugging values we get

$1,000,000= 300(1+\frac{0.75}{100})^n$

solving the above equation we get

n = 436 months

which is equal to 36.33 years.