Question

Susie wants to deposit $6000 into a savings account and plans to leave her money in the account for 10 years. The bank offers two types of savings accounts
• Account 1: offers 4.5% simple interest.
• Account 2: offers 4% interest compounded annually.

Which statement about the savings accounts is true?

A. Susie should invest her money in Account 1 because the account will earn $300.00 more in interest than Account 2 after 10 years.
B. Susie should invest her money in Account 1 because the account will earn $436.35 more in interest than Account 2 after 10 years.
C. Susie should invest her money in Account 2 because the account will earn $617.82 more in interest than Account 1 after 10 years.
D. Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years.

Answer 1

Answer:

Option D

Step-by-step explanation:

step 1

Account 1

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

$t=10\ years\\ P=\ 6,000\\r=4.5\%=4.5/100=0.045$

substitute in the formula above

$A=6,000(1+0.045*10)$

$A=6,000(1.45)$

$A=\ 8,700$

step 2

Account 2

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

$t=10\ years\\ P=\ 6,000\\ r=4\%=4/100=0.04\\n=1$  

substitute in the formula above

$A=6,000(1+\frac{0.04}{1})^{1*10}$  

$A=6,000(1.04)^{10}$  

$A=\ 8,881.47$  

step 3

Find the difference

$\ 8,881.47-\ 8,700=\ 181.47$

therefore

Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years