a savings account at bank a pays 5% simple interest. an account at bank b pays 2% compound interest. the…
a savings account at bank a pays 5% simple interest. an account at bank b pays 2% compound interest. the table shows the balance in each account after an initial deposit of $1000. which describes the balances after a long period of time? year bank a bank b 1 $1000 $1000 2 $1050 $1020 3 $1100 $1040.40 4 $1150 $1061.21 5 $1200 $1082.43 a. the balances will be the same. b. the balance in bank a will be greater. c. the balance in bank b will be greater.
Answer
Explanation:
Step1: Recall simple - interest formula
The simple - interest formula is $A = P(1+rt)$, where $P=$1000$, $r = 0.05$ (5% interest rate), and $t$ is the number of years. So $A_A=1000(1 + 0.05t)=1000+50t$.
Step2: Recall compound - interest formula
The compound - interest formula is $A = P(1 + r)^t$, where $P = 1000$, $r=0.02$ (2% interest rate). So $A_B = 1000(1 + 0.02)^t=1000\times1.02^t$.
Step3: Analyze long - term behavior
As $t$ gets very large, the function $y = 1000+50t$ (linear function) and $y = 1000\times1.02^t$ (exponential function). The exponential function $y = a\times b^t$ ($a = 1000$, $b=1.02>1$) will grow faster than the linear function $y=mx + c$ ($m = 50$, $c = 1000$) in the long - run.
Answer:
C. The balance in Bank B will be greater.