Question

You need to accumulate $10,000. To do so, you plan to make deposits of $1,000 per year - with the first payment being made a year from today - into a bank account that pays 14% annual interest. Your last deposit will be less than $1,000 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal

Answer 1

It will take 6.68 years to reach the $10,000 goal.

Step-by-step explanation:

As the deposit of $1,000 per year is a form of the annuity payment.

We will use the following formula in order to calculate the numbers of year required to reach the goal

Future value of Annuity = Annuity payment x ( ( ( 1 + interest rate )^numbers of years ) - 1 ) / Interest rate

Where

Future value of Annuity = Target amount = $10,000

Annuity payment = Yearly deposti = $1,000

Interest rate = 14%

Numbers of years = n = ?

Placing values in the formula

Future value of Annuity = Annuity payment x ( ( ( 1 + interest rate )^numbers of years ) - 1 ) / Interest rate

$10,000 = $1,000 x ( ( ( 1 + 14% )^n ) - 1 ) /14%

$10,000 x 14% = $1,000 x ( ( ( 1.14 )^n ) - 1)

$1,400 = $1,000 x ( ( ( 1.14 )^n ) - 1)

$1,400 / $1,000 = ( ( 1.14 )^n ) - 1

1.4 = ( ( 1.14 )^n ) - 1

1.4 + 1 = 1.14^n

2.4 = 1.14^n

Log 2.4 = n x Log 1.14

n = Log 2.4 / Log 1.14

n = 6.681525965

n = 6.68 years

It will take 6.68 years to reach the $10,000 goal.