gabriel deposits $2,500 into each of two savings accounts. account i earns 4% annual simple interest…
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?
Answer
Explanation:
Step1: Calculate balance of Account I
The simple - interest formula is $A = P(1+rt)$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. Given $P = 2500$, $r=0.04$, and $t = 3$. $A_1=2500(1 + 0.04\times3)=2500(1 + 0.12)=2500\times1.12 = 2800$.
Step2: Calculate balance of Account II
The compound - interest formula is $A=P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. Given $P = 2500$, $r = 0.04$, and $t=3$. $A_2=2500(1 + 0.04)^3=2500\times1.04^3=2500\times1.124864 = 2812.16$.
Step3: Calculate the sum of the two balances
$A=A_1 + A_2=2800+2812.16 = 5612.16$.
Answer:
$5612.16$