A deposit of $ 5000 is made in an account that earns 4 % interest compounded quarterly.The balance in the account after n quarters is given by $$A _ { n } = 5000 \left( 1 + \frac { 0.04 } { 4 } \right) ^ { n } , n = 1,2,3 , \ldots$$ Find the balance in the account after 10 years by finding the 40th term of the sequence.Round to the nearest penny.
A)$ 7518.76
B)$ 7370.61
C)$ 7444.32
D)$ 24,005.10

Question

Quizplus · Accepted Answer

We are given that the deposit is $5000 and the interest rate is 4%, compounded quarterly. This means that the interest rate per quarter is 1%. Therefore, the formula for the balance after n quarters is:

Balance = 5000(1 + 0.01)^n

To find the balance after 10 years (which is equivalent to 40 quarters), we can substitute n = 40 into the formula:

Balance = 5000(1 + 0.01)^40
Balance = $7444.32 (rounded to the nearest penny)

Therefore, the best choice is C.

A Deposit of $ 5000 Is Made in an Account An=5000(1+0.044)n,n=1,2,3,…A _ { n } = 5000 \left( 1 + \frac { 0.04 } { 4 } \right) ^ { n } , n = 1,2,3 , \ldotsAn​=5000(1+40.04​)n,n=1,2,3,…

A Deposit of $ 5000 Is Made in an Account $A _ { n } = 5000 \left( 1 + \frac { 0.04 } { 4 } \right) ^ { n } , n = 1,2,3 , \ldots$