matthew invested $5000 in an account that earns 3.8% interest . how much did matthew have in his account after 3 years

Given that :- invested amount(principal amount)=$5000

interest rate(r) = 3.8%per annum 

amount after 3 year(t)=?

Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal. Further, the interest calculation for the next time period is on the accumulated principal value. 

The compound interest is calculated at regular intervals like annually(yearly), semi-annually, quarterly, monthly, etc;  The compound interest is calculated, after calculating the total amount over a period of time, based on the rate of interest, and the initial principal. For an initial principal of P, rate of interest per annum of r, time period t in years, frequency of the number of times the interest is compounded annually n, the formula for calculation of amount is as follows

The above formula represents the total amount at the end of the time period and includes the compounded interest and the principal. Further, we can calculate the compound interest by subtracting the principal from this amount. The formula for calculating the compound interest is as follows 

Compound interest formula => A=P(1+r/n)^nt where, P is the principal amount, r is the rate of interest(decimal), n is frequency or no. of  times the interest is compounded annually, t is the overall tenure.

It is to be noted that the above-given formula is the general formula when the principal is compounded n number of times in a year. If the given principal is compounded annually, the amount after the time period at percent rate of interest, r, is given as:

A = P(1 + r/100)^t

A=5000(1+3.8/100)^3

A=5000(1+0.038)^3

A=5000(1.038)^3

A=5000(1.1183)

A=5591.5   (amount matthew have in his account after 3 years)