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Answer:
(a) After 5 years, the amount in Jose's account can be calculated using the formula for compound interest:
A=P(1+/r/n)^nt
where:
: A is the amount of money accumulated after n years, including interest.
: P is the principal amount (the initial amount Jose invested), which is $3800.
:r is the annual interest rate (1.43% or 0.0143 in decimal form).
:n is the number of times the interest is compounded per year (monthly compounding means =12)
:t is the number of years the money is invested for, which is 5 years.
Substitute the values into the formula and calculate:
A=3800(1+0.0143/12)^(12∗5)
A=3800(1+ 0.0143/12)^60
A≈3800×1.072382
A≈4078.63
Therefore, after 5 years, there will be approximately $4078.63 in Jose's account.
(b) To calculate the interest earned on Jose's investment after 5 years, subtract the principal amount from the total amount:
Interest Earned= A−P
Interest Earned= 4078.63 −3800
Interest Earned≈ 278.63
Hence, the interest earned on Jose's investment after 5 years is approximately $278.63.