Question

Mr. Bass checked his savings account and saw he had a balance of $2155.00. The account earns 6%, compounded quarterly. What is the equation to represent the balance in this account? How much will he have in the account in 8 years? Round to the nearest penny.

Equation:
a) B = 2155 * (1 + 0.06/4)^(48)
b) B = 2155 * (1 + 0.06)^8
c) B = 2155 * (1 + 0.06/4)^(84)
d) B = 2155 * (1 + 0.06/8)^(4*8)

Balance in 8 years:
a) $3,035.50
b) $2,845.78
c) $2,587.34
d) $2,436.25

Bonus: If he opened the account five years ago, how much did he start with? Round to the nearest penny.
a) $1,750.23
b) $1,827.64
c) $1,934.58
d) $1,984.62

Answer 1

The equation to represent the balance in Mr. Bass's account is B = 2155 * (1 + 0.06/4)^(48). After 8 years, Mr. Bass will have $3035.50 in his account. If he opened the account five years ago, he started with $1,827.64.

Step-by-step explanation:

The equation to represent the balance in Mr. Bass's account is an option a) B = 2155 * (1 + 0.06/4)^(48). This equation takes into account the initial balance of $2155.00 and the interest rate of 6%, compounded quarterly. To calculate the balance in the account after 8 years, we plug in the values into the equation:

B = 2155 * (1 + 0.06/4)^(4*8)

Simplifying this expression gives B = $3035.50, which is option a) in the given choices. Therefore, Mr. Bass will have $3035.50 in his account after 8 years.

To calculate how much Mr. Bass started with if he opened the account five years ago, we need to work backward and use the compound interest formula. Plugging in the values into the formula:

P = B / (1 + 0.06/4)^(4*5)

We get P = $1833.50, which rounds to the nearest penny as $1,827.64, option b) in the given choices.