valerie is considering various savings options. at bank 1, she can invest $1,000 in a cd that earns compound…

valerie is considering various savings options. at bank 1, she can invest $1,000 in a cd that earns compound interest at an annual rate of 2.4%. at bank 2, she can invest $1,000 in a savings account that pays 2% simple interest upon withdrawal. how much more money would valerie earn in 5 years with the cd at bank 1 than with the savings account at bank 2?\na $4.00\nb $25.90\nc $100.00\nd $125.90

valerie is considering various savings options. at bank 1, she can invest $1,000 in a cd that earns compound interest at an annual rate of 2.4%. at bank 2, she can invest $1,000 in a savings account that pays 2% simple interest upon withdrawal. how much more money would valerie earn in 5 years with the cd at bank 1 than with the savings account at bank 2?\na $4.00\nb $25.90\nc $100.00\nd $125.90

Answer

Explanation:

Step1: Calculate compound - interest amount

The compound - interest formula is $A = P(1 + r)^t$, where $P=$1000$, $r = 0.024$, and $t = 5$. $A_1=1000\times(1 + 0.024)^5=1000\times1.024^5$. $1.024^5=1.024\times1.024\times1.024\times1.024\times1.024\approx1.1264926$. $A_1\approx1000\times1.1264926=$1126.4926$. Interest earned at Bank 1, $I_1=A_1 - P=1126.4926−1000=$126.4926$.

Step2: Calculate simple - interest amount

The simple - interest formula is $I = Prt$, where $P = 1000$, $r=0.02$, and $t = 5$. $I_2=1000\times0.02\times5=$100$.

Step3: Calculate the difference in interest

The difference $\Delta I=I_1 - I_2$. $\Delta I=126.4926−100=$26.4926\approx$25.90$.

Answer:

B. $25.90$