Question

Royce deposits $1200 into a savings account that has an annual simple interest rate of 1.1%. After one year, he deposits another $1200 into the account.

How much interest will Royce have earned at the end of the first year?

Answer 1

Explanation:

Using simple interest, it is found that:Royce will have earned $13.2 of interest after the first year.Royce will have earned $39.4 of total interest at the end of the second year.The total amount in the account at the end of the second year will be of $2,439.60.Simple InterestSimple interest is used when there is a single compounding per time period, which is usually measured in years.The balance of an account after t time periods in is modeled by:A(t) = P(1 + rt)In which:P is the initial balance of the account/initial investment.r is the interest rate, as a decimal.The interest accrued after t years is given as follows:I(t) = Prt.For the first year, the parameters are as follows:P = 1200, r = 0.011, t = 1.Hence the interest is:I(1) = 1200 x 0.011 = $13.2.The total interest at the end of the second year is given by the sum of:$13.2 of interest from the second deposit.From the first deposit, I(2) = 1200 x 0.011 x 2 = 26.4.Hence:13.2 + 26.4 = $39.6.The total amount at the end of the second year is composed as follows:$2,400: two deposits of $1,200.$39.6 of interest.Hence:2400 + 39.6 - $2,439.60.