Question

we have that a loan of $6000 is given at an interest rate of 17% compounded each year. compound interest is interest based on the original amount and the past interest owed. (a) find the amount owed at the end of 1 year. during the first year, there is no past interest to consider. this means that interest is owed for the original amount only. so, to compute the interest owed at the end of 1 year, we multiply $6000 by 17%. since 17% = 0.17, we get the following. 17% of $6000 = 0.17·$6000 = $1020 we add this interest to the original amount to find the total amount owed at the end of 1 year. $6000 + $1020 = $7020 so, the amount owed at the end of 1 year is $7020. (b) find the amount owed at the end of 2 years. the interest is compounded each year. so, the interest for the second year is based on the amount owed after the first year. that is, the interest for the second year is computed based on $7020. computing the interest for the second year, we get the following. 17% of $7020 = 0.17·$7020 = $1193.40 then we add this interest to the amount owed at the end of 1 year. $7020 + $1193.40 = $8213.40 so, the amount owed at the end of 2 years is $8213.40.

Explanation:

Step1: Calculate 1 - year interest

The original loan is $P = 6000$ and the annual - interest rate $r=0.17$. The interest $I_1$ for the first year is $I_1 = P\times r=6000\times0.17 = 1020$.

Step2: Find 1 - year amount

The amount $A_1$ owed at the end of 1 year is the sum of the original loan and the first - year interest. So $A_1=P + I_1=6000 + 1020=7020$.

Step3: Calculate 2 - year interest

The principal for the second year is $A_1 = 7020$. The interest $I_2$ for the second year is $I_2=A_1\times r=7020\times0.17 = 1193.4$.

Step4: Find 2 - year amount

The amount $A_2$ owed at the end of 2 years is the sum of the amount owed at the end of 1 year and the second - year interest. So $A_2=A_1+I_2=7020 + 1193.4=8213.4$.

Answer:

(a) $7020
(b) $8213.40