Zenda deposited $1,200 in a savings account that pays 6.5% interest,
compounded monthly. What is the balance in her account at the
beginning of the third month?
a. $1,213.04
b. $1,511.65
c. $1,206.50
d. $1,296
To solve this problem, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount
- P is the principal (initial amount)
- r is the annual interest rate (as a decimal)
- n is the number of times the interest is compounded per year
- t is the time (in years)
In this case, P = $1,200, r = 0.065 (6.5% as a decimal), n = 12 (monthly compounding), and t = 2/12 (two months, expressed in years as 2/12). Plugging these values into the formula, we get:
A = 1200(1 + 0.065/12)^(12/6)
A = 1200(1.005416667)^2
A = $1,213.04
Therefore, the answer is (a) $1,213.04.
To calculate the balance in Zenda's account at the beginning of the third month, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount (balance) in the account
P = the initial deposit ($1,200)
r = the annual interest rate (6.5% or 0.065)
n = the number of times interest is compounded per year (monthly compounding, so n = 12)
t = the number of years (in this case, 2 months or 2/12 years)
Let's substitute the values into the formula and calculate the balance:
A = 1200(1 + 0.065/12)^(12*(2/12))
A = 1200(1 + 0.00541667)^(2)
A = 1200(1.00541667)^(2)
A ≈ 1200(1.01088361)
A ≈ 1212.96
Therefore, the balance in Zenda's account at the beginning of the third month is approximately $1,212.96.
Among the answer choices, the closest amount is $1,213.04 (option a).
To find the balance in Zenda's account at the beginning of the third month, we need to calculate the compound interest and add it to the principal.
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $1,200
r = 6.5% = 0.065 (since the annual interest rate is given as a percentage, we divide it by 100 to convert it to a decimal)
n = 12 (since interest is compounded monthly)
t = 2 (since we want to find the balance at the beginning of the third month)
Plugging these values into the formula, we get:
A = 1200(1 + 0.065/12)^(12*2)
Calculating the exponential part first:
(1 + 0.065/12)^(12*2) = (1 + 0.00541666667)^24 = 1.1370580292
Now, multiply the principal by the exponential factor to get the final amount:
A = 1200 * 1.1370580292 = $1,364.47 (rounded to 2 decimal places)
Therefore, the balance in Zenda's account at the beginning of the third month is approximately $1,364.47. None of the given options exactly matches this amount, but the closest option is d. $1,296.