$2500 is invested at 4% interest compounded monthly. How much is in… Step by Step

Step by step

The question

Question: $2500 is invested at 4% interest compounded monthly.

How much is in the account after 10 years?

1 Read the numbers

P is the money put in: $2500.

P = $2500: the money put in

r is the rate.

4% is 4/100: 0.04.

r = 4% = 0.04

n is how many times a year the interest is added: monthly, so n = 12.

n = 12: monthly: 12 times a year

t is the time in years: 10.

t = 10 years

The amount after t years is A = P times (1 + r/n) to the power nt.

Each time, the money is multiplied by 1 + r over n.

A = P(1 + rn)^nt

Careful!

The 4% is for a whole year.

Each time we add only r/n: 0.04 divided by 12.

Careful: not 2500 × 1.04¹²⁰ ✗

2 Put them in

We put the numbers in.

A = 2500(1 + 0.0412)^{12 × 10}

3 Work it out

Inside the bracket first: 0.04 divided by 12 is about 0.00333333.

The power: 12 times 10 is 120.

0.04 ÷ 12 ≈ 0.00333333

12 × 10 = 120

So A is 2500 times the bracket to the power 120.

A = 2500 × (1 + 0.0412)¹²⁰

With a calculator, that power is about 1.49083.

(1 + 0.0412)¹²⁰ ≈ 1.49083

Now times 2500.

A ≈ 2500 × 1.49083

3727.0817...

Money is rounded to cents: about $3727.08.

A ≈ $3727.08

4 Check

Let's check by going back: 3727.08 divided by 1.49083 is about $2500, the money put in.

$3727.08 ÷ 1.49083 ≈ $2500

And it makes sense.

Simple interest would give $3500.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $2500 + $1000 = $3500 < $3727.08

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer