Gabriel deposits $2,500 into each of two savings accounts.
• Account I earns 4% annual simple interest.
• Account II earns 4% interest compounded annually.
Gabriel does not make any additional deposits or withdrawals.
What is the sum of the balances of Account I and Account II at the end of 3 years?
A) $5,600.00
B) $5,612.16
C) $5,624.32
D) $5,200.00

Option B) $5,612.16

Step-by-step explanation:

Part 1) Account I earns 4% annual simple interest.

we know that

The simple interest formula is equal to

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

substitute in the formula above

Part 2) Account II earns 4% interest compounded annually.

we know that    

The compound interest formula is equal to  

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  

substitute in the formula above  

Part 3) What is the sum of the balances of Account I and Account II at the end of 3 years?

Sum the two final investment

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation:

so, converting firstly the mixed fractions to improper fractions and then "adding".