$1500 is invested at 4% interest compounded daily. How much is in… Step by Step

Step by step

The question

Question: $1500 is invested at 4% interest compounded daily.

How much is in the account after 2 years?

1 Read the numbers

P is the money put in: $1500.

P = $1500: 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: daily, so n = 365.

n = 365: daily: 365 times a year

t is the time in years: 2.

t = 2 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 365.

Careful: not 1500 × 1.04⁷³⁰ ✗

2 Put them in

We put the numbers in.

A = 1500(1 + 0.04365)^{365 × 2}

3 Work it out

Inside the bracket first: 0.04 divided by 365 is about 0.000109589.

The power: 365 times 2 is 730.

0.04 ÷ 365 ≈ 0.000109589

365 × 2 = 730

So A is 1500 times the bracket to the power 730.

A = 1500 × (1 + 0.04365)⁷³⁰

With a calculator, that power is about 1.08328.

(1 + 0.04365)⁷³⁰ ≈ 1.08328

Now times 1500.

A ≈ 1500 × 1.08328

1624.9235...

Money is rounded to cents: about $1624.92.

A ≈ $1624.92

4 Check

Let's check by going back: 1624.92 divided by 1.08328 is about $1500, the money put in.

$1624.92 ÷ 1.08328 ≈ $1500

And it makes sense.

Simple interest would give $1620.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $1500 + $120 = $1620 < $1624.92

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer