Question

4 a savings account offers an annual simple interest rate of 1.5% if you deposit money before a certain date. after that date, the rate drops to 1%. ms. byrne deposits $8200 into the account after the deadline. how much interest will she lose after 6 months by missing the deadline?
5 harry borrowed $24 000 at an annual simple interest rate of 2%. how much more does he need to pay back if he takes 5 years than if he takes 3 years to repay his loan?
6 jamal borrowed $15 600 for 6 years from a bank. the annual simple interest rate for the first 3 years is 1.6%. from then onward, the annual simple interest rate is increased to 2%. how much interest will he owe at the end of 6 years?
7 ervin deposited $3000 into a bank. the bank gives an interest rate of 4% compounded yearly. how much money will be in ervins account after 6 years? give your answer to the nearest cent.
8 shani borrowed $5000 at an annual interest rate of 4% compounded yearly. william borrowed the same amount of money at an annual interest rate of 6% compounded yearly how much more interest will william pay than shani at the end of 3 years?

Explanation:

Let's solve question 4 first.

Step1: Recall simple interest formula

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years.

Step2: Calculate interest at 1.5% for 6 months

First, convert 6 months to years: $t = \frac{6}{12} = 0.5$ years.
Principal $P = 8200$, rate $r_1 = 1.5\% = 0.015$.
Interest at 1.5%: $I_1 = 8200 \times 0.015 \times 0.5$.
Calculate $8200 \times 0.015 = 123$, then $123 \times 0.5 = 61.5$.

Step3: Calculate interest at 1% for 6 months

Rate $r_2 = 1\% = 0.01$.
Interest at 1%: $I_2 = 8200 \times 0.01 \times 0.5$.
Calculate $8200 \times 0.01 = 82$, then $82 \times 0.5 = 41$.

Step4: Find the interest lost

Interest lost = $I_1 - I_2 = 61.5 - 41 = 20.5$.

Answer:

The interest she will lose is $\$20.50$.