Tanya is 42 years old. she would like to open aretirement account so she will have half a million dollars in the account when she retires at the age 65. how much did she deposit each month into an account with an apr of 2.75% to reach her goal?

Let the total amount that Sarah deposited be $x

using the annuity formula:

A=P[ ((1+r) ^n-1) / r]

A=future value

r=rate

n=number of years

from the information given:

A=$500000

r=2.75%

n=65-42=23 years

p=$x

thus plugging our values in the formula we get:

500000=x[ ((1+0.0275) ^ (23) - 1) / (0.0275) ]

500000=31.50x

x=15,872.04883

She deposited 15,873.04883 per year

The monthly deposit will therefore be:

15873.04883/12=$1322.67