suppose ivanna borrows $1500 at an interest rate of 6% compounded each year. assume that no payments are…
suppose ivanna borrows $1500 at an interest rate of 6% compounded each year. assume that no payments are made on the loan. follow the instructions below, do not do any rounding. (a) find the amount owed at the end of 1 year. $ (b) find the amount owed at the end of 2 years. $
Answer
Explanation:
Step1: Recall compound - interest formula
The compound - interest formula is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Here, $P=$1500$, $r = 0.06$ (since $6%=0.06$).
Step2: Calculate amount owed at the end of 1 year
Substitute $P = 1500$, $r=0.06$, and $t = 1$ into the formula $A = P(1 + r)^t$. $A_1=1500\times(1 + 0.06)^1=1500\times1.06 = 1590$
Step3: Calculate amount owed at the end of 2 years
Substitute $P = 1500$, $r = 0.06$, and $t = 2$ into the formula $A = P(1 + r)^t$. $A_2=1500\times(1 + 0.06)^2=1500\times1.06^2=1500\times1.1236 = 1685.4$
Answer:
(a) $1590$ (b) $1685.4$