Q:

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.

Accepted Solution

A:
Answer:Frederick collects the an amount of $4813.24 at the age of 18 out of which $2000 was the beginning amount.Step-by-step explanation:We are given the following information in the question:Amount = 2000Interest rate = 5%The money is compounded annually or yearly.Time = 18 yearsCompound interest = [tex]A = P\bigg(1+\displaystyle\frac{r}{n}\bigg)^{nt}[/tex]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,[tex]A = P\bigg(1+\displaystyle\frac{r}{n}\bigg)^{nt}\\\\A = 2000\bigg(1+\frac{5}{100}\bigg)^{18}\\\\A = 4813.24\\\\\text{Interest, I} = \text{Amount - Principal} = A - P\\\\I = 4813.24 - 2000 = 2813.24[/tex]Thus, Frederick collects the an amount of $4813.24 at the age of 18 out of which $2000 was the beginning amount.