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A bank offers an investment account with an annual interest rate of 1.43% compounded monthly. Jose invests $3800 into the account for 5 years. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent.
(a) Assuming no withdrawals are made, how much money is in Jose's account after 5 years?
(b) How much interest is earned on Jose's investment after 5 years?

Sagot :

ganaahmed

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.

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