A deposit of $ 5000 is made in an account that earns 8 % interest compounded monthly.The balance in the account after n months is given by $$A _ { n } = 5000 \left( 1 + \frac { 0.08 } { 12 } \right) ^ { n } , n = 1,2,3 , \ldots$$ Find the balance in the account after 8 years by finding the 96th term of the sequence.Round to the nearest penny.
A)$ 8,084,450.96
B)$ 9462.29
C)$ 9399.62
D)$ 483200.00
E)$ 9525.37

Question

Quizplus · Accepted Answer

To find the balance after 8 years (which is 96 months since 8 years * 12 months/year = 96 months), we substitute $n = 96$ into the given formula: $$A_{96} = 5000 \left(1 + \frac{0.08}{12}\right)^{96}$$. Calculating this gives approximately $9462.29.

A Deposit of $ 5000 Is Made in an Account An=5000(1+0.0812)n,n=1,2,3,…A _ { n } = 5000 \left( 1 + \frac { 0.08 } { 12 } \right) ^ { n } , n = 1,2,3 , \ldotsAn​=5000(1+120.08​)n,n=1,2,3,…

A Deposit of $ 5000 Is Made in an Account $A _ { n } = 5000 \left( 1 + \frac { 0.08 } { 12 } \right) ^ { n } , n = 1,2,3 , \ldots$