Question

When Frederick was born, his grandparents gave him a gift of 2000, which was invested at an interest rate of 5% per year, compounded yearly. How much money will Frederick have when he collects the money at the age of 18? Give your answer to the nearest hundredth of a dollar.

Answer 1

$4813.24

Explanation:

Five percent growth corresponds to multiplication by 1+5%=1.05. So, the amount of money Frederick will have in 18 years is 2000(1+.05)^18= $4813.24

Answer 2

Frederick collects the an amount of $4813.24 at the age of 18 out of which $2000 was the beginning amount.

Explanation:

We are given the following information in the question:

Amount = 2000

Interest rate = 5%

The money is compounded annually or yearly.

Time = 18 years

Compound interest =

`A = P\bigg(1+\displaystyle(r)/(n)\bigg)^(nt)`

where P is the principal amount, r is the interest rate, t is the time in years and n is the number of compounding in a year.

Since, the money is compounded yearly we put n = 1.

Putting all the values, we get,

`A = P\bigg(1+\displaystyle(r)/(n)\bigg)^(nt)\\\\A = 2000\bigg(1+(5)/(100)\bigg)^(18)\\\\A = 4813.24\\\\\text{Interest, I} = \text{Amount - Principal} = A - P\\\\I = 4813.24 - 2000 = 2813.24`

Thus, Frederick collects the an amount of $4813.24 at the age of 18 out of which $2000 was the beginning amount.