Question

To save for retirement, you decide to deposit $1,000 into an IRA at the end of each year for the next 30 years. If this savings annuity has an interest rate of 10% per year compounded annually, then how much interest will you earn over the course of the 30 years?

Answer 1

Answer:

134494

Step-by-step explanation:

Answer 2

Answer: 134,494

Step-by-step explanation: d=$1,000, the yearly deposit.

r=0.10, or a 10% annual rate.

k=1, since we’re doing yearly deposits and we’ll compound yearly.

N=30, we want the amount after 30 years.

Putting this into the annuity formula:

PN=d⋅((1+rk)N⋅k−1)rkP30=1,000⋅((1+0.101)30⋅1−1)(0.101)P30=1,000⋅((1.1)30−1)(0.10)P30=1,000⋅(17.4494−1)(0.10)P30=1,000⋅(16.4494)(0.10)=$164,494.

The account will grow to $164,494 after 30 years.

Notice that you deposited into the account a total of $30,000 ($1,000 a year for 30 years). The difference between what you end up with and how much you put in is the interest earned. In this case it is $164,494–$30,000=$134,494.