Question

On her 30th birthday, Ann Marie opened a new compound interest account with $25,000

to save for her retirement.

The account pays 5% interest annually.

No further deposit is made to the account and no withdrawals are made.

If Ann Marie retires on her 60th birthday and close the account at that time, how much interest would she have earned on her initial $25,000? (Round your answer to the nearest cent).

Answer 1

The interest in 30 years be 8305000 cent.

Explanation:

Formula

`Amount = P(1+r)^(t)`

Where P is the principle , r is the rate of interest in the decimal form and t is the time.

As given

On her 30th birthday, Ann Marie opened a new compound interest account with $25,000.

The account pays 5% interest annually.

If Ann Marie retires on her 60th birthday and close the account at that time .

P = $25000

5% is written in the decimal form.

`= (5)/(100)`

= 0.05

r = 0.05

As Ann Marie open account on his 30 th birthday and close it at its 60 th birthday .

Thus

t = 60 - 30

t = 30 years

Put all the value in the formula

`Amount = 25000(1+0.05)^(30)`

`Amount = 25000(1.05)^(30)`

`Amount = 25000* 4.322 (Approx)`

`Amount = \$ 108050`

As

Amount = Principle + Interest

Putting the value

$108050 = $25000+ Interest

$108050 - $25000 = Interest

Interest = $83050

As 1 dollar = 100 cent

Convert $83050 convert into cent .

$83050 = 83050 × 100

= 8305000 cent.

Therefore the interest in 30 years be 8305000 cent.

Answer 2

On her 60th birthday, she would have earned $83048.5.

Explanation:

The formula to calculate the compound interest is:

`A=P(1+(r)/(100) )^(n)` --- (1)

where A is Principal and interest, r is the rate of interest and n is the number of years compounded.

For our problem,

P = 25000,

r = 0.05 and

n = 60 - 30 = 30

Substitute these values in (1), we get,

`A=25000(1+0.05)^(30)`

`=25000(1.05)^(30)`

= 25000(4.32194)

= 108048.5

Compound Interest = Amount - Principal

= 108048.5 - 25000

= 83048.50

Hence, on her 60th birthday, she would have earned $83048.5.