$300 is deposited at the end of each quarter into an account paying… Step by Step

Step by step

The question

Question: $300 is deposited at the end of each quarter into an account paying 8% compounded quarterly.

How much is in the account after 10 years?

1 Read the numbers

PMT is the money put in each time: $300.

r is the yearly rate: 8% is 0.08.

PMT = $300 each time, r = 8% = 0.08

n is how many times a year: 4.

t is the time: 10 years.

n = 4 a year, t = 10 years

2 Per payment

Interest is added each quarter.

The rate for one quarter is i: r over n.

0.08 divided by 4 is 0.02.

i = rn = 0.084 = 0.02

i = the rate each quarter

And N is how many deposits: 4 times 10 is 40.

N = n × t = 4 × 10 = 40

3 Use the formula

The future value FV is what the account holds at the end: PMT times, (1 + i) to the power N, minus 1, over i.

FV = PMT × (1 + i)^N − 1i

FV = future value: the money at the end

We put the numbers in: 1 plus 0.02 is 1.02.

FV = 300 × 1.02⁴⁰ − 10.02

4 Work it out

With a calculator, 1.02 to the power 40 is about 2.20804.

Minus 1, divided by 0.02: about 60.402.

1.02⁴⁰ ≈ 2.20804

(2.20804 − 1) ÷ 0.02 ≈ 60.402

So FV is 300 times 60.402.

FV ≈ 300 × 60.402

Money is rounded to cents: about 18120 dollars and 59 cents.

FV ≈ $18,120.59

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $300 × 40 ✗

5 Check

Let's check.

The deposits alone are 300 times 40: $12000.

The account has more, because of the interest.

deposits: $300 × 40 = $12,000 < $18,120.59

The interest earned is 6120 dollars and 59 cents.

So it makes sense!

interest: $18,120.59 − $12,000 = $6,120.59

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer