Final answer:
a. the first quarter's interest is $3,528.06.
b. the first quarter's ending balance is $7,028.06.
c. the second quarter's interest is $7,097.84.
d. the second quarter's ending balance is $14,125.90.
e. the third quarter's interest is $14,213.02
f. the third quarter's ending balance is $28,338.92.
g. the fourth quarter's interest is $28,468.97.
h. the balance at the end of 1 year is $64,111.55.
i. the interest in the first year is $29,611.55.
Step-by-step explanation:
a) To find the first quarter's interest, we can use the formula for compound interest:
Interest = Principal Amount * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Plugging in the values from the question:
Principal Amount = $3,500
Rate = 0.8%
Number of Compounding Periods = 4 (quarterly)
Time = 1 quarter
Interest = $3,500 * (1 + 0.008/4)^(4*1)
Interest = $3,500 * (1.002)^4
Interest = $3,500 * 1.008016032064
Interest = $3,528.06
Therefore, the first quarter's interest is $3,528.06.
b) To find the first quarter's ending balance, we add the interest to the principal amount:
Ending Balance = Principal Amount + Interest
Ending Balance = $3,500 + $3,528.06
Ending Balance = $7,028.06
Therefore, the first quarter's ending balance is $7,028.06.
c) d)) To find the second quarter's interest and ending balance, we need to repeat the process using the new principal amount of $7,028.06. We can use the same formula and plug in the values:
Principal Amount = $7,028.06
Rate = 0.8%
Number of Compounding Periods = 4 (quarterly)
Time = 1 quarter
Interest = $7,028.06 * (1 + 0.008/4)^(4*1)
Interest = $7,028.06 * (1.002)^4
Interest = $7,028.06 * 1.008016032064
Interest = $7,097.84
Ending Balance = Principal Amount + Interest
Ending Balance = $7,028.06 + $7,097.84
Ending Balance = $14,125.90
Therefore, the second quarter's interest is $7,097.84 and the ending balance is $14,125.90.
e) f)) g)) To find the third and fourth quarter's interest and ending balance, we repeat the same process using the new principal amount for each quarter. Here are the results:
Third Quarter: Interest = $14,125.90 * (1 + 0.008/4)^(4*1)
Interest = $14,125.90 * (1.002)^4
Interest = $14,125.90 * 1.008016032064
Interest = $14,213.02
Ending Balance = Principal Amount + Interest
Ending Balance = $14,125.90 + $14,213.02
Ending Balance = $28,338.92
Fourth Quarter: Interest = $28,338.92 * (1 + 0.008/4)^(4*1)
Interest = $28,338.92 * (1.002)^4
Interest = $28,338.92 * 1.008016032064
Interest = $28,468.97
Ending Balance = Principal Amount + Interest
Ending Balance = $28,338.92 + $28,468.97
Ending Balance = $56,807.89
Therefore, the third quarter's interest is $14,213.02, the ending balance is $28,338.92. And the fourth quarter's interest is $28,468.97 and the ending balance is $56,807.89.
h) To find the balance at the end of 1 year, we can use the same formula one more time:
Principal Amount = $56,807.89
Rate = 0.8%
Number of Compounding Periods = 4 (quarterly)
Time = 1 year = 4 quarters
Ending Balance = Principal Amount * (1 + Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)
Ending Balance = $56,807.89 * (1 + 0.008/4)^(4*4)
Ending Balance = $56,807.89 * (1.002)^16
Ending Balance = $56,807.89 * 1.12805406493
Ending Balance = $64,111.55
Therefore, the balance at the end of 1 year is $64,111.55.
i) To find the total interest earned in the first year, we can subtract the principal amount from the ending balance:
Total Interest = Ending Balance - Principal Amount
Total Interest = $64,111.55 - $35,00
Total Interest = $29,611.55
Therefore, the account earns $29,611.55 in the first year.