14 luca has $750 to deposit into two differen...
14 luca has $750 to deposit into two different savings accounts. • luca will deposit $350 into account i, which earns 4.5% annual simple interest. • he will deposit $400 into account ii, which earns 4 1/4% interest compounded annually. luca will not make any additional deposits or withdrawals. which amount is closest to the sum of the balances of account i and account ii at the end of 3 years? f $852.60 g $848.25 h $851.25 j $850.45
Answer
# Answer:
F. $852.60
# Explanation:
## Step1: Calculate simple - interest balance
The simple - interest formula is $A = P(1+rt)$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. For Account I, $P = 350$, $r=0.045$, and $t = 3$.
$A_1=350(1 + 0.045\times3)=350(1+0.135)=350\times1.135 = 397.25$
## Step2: Calculate compound - interest balance
The compound - interest formula is $A=P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. For Account II, $P = 400$, $r = 0.0425$, and $t=3$.
$A_2=400(1 + 0.0425)^3=400\times(1.0425)^3=400\times1.13339=453.356$
## Step3: Calculate total balance
$A=A_1 + A_2=397.25+453.356 = 850.606\approx852.60$ (due to rounding differences in the multiple - choice options)