Question

Suppose you decide to deposit $16,000 into a savings account that pays a nominal rate of 7.80%, but interest is compounded daily. Based on a 365-day year, how much would you have in your account after six months? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$16,304.43

$16,470.80

$16,637.17

$16,969.91

Answer 1

Given that;
Principal amount is $16,000
Interest rate is 7.80%
Number of compounds per year is 365
Time period is 6 months, so the number of periods is (6/12)*365 =182.5
Here 12 refers to the total number of months in a year and 365 is the number of days.
So, total number of periods is 182.5

Amount = (Principal)*[1 + (Interest rate)/n]^(Number of periods)
Here, n refers to number of compounds per year.
Substituting the values, we get;
Amount = (16000)*[1 + (7.80%)/365]^(182.5)
= (16000)*[1 + 0.000213699]^(182.5)
= (16000)*(1.000213699)^(182.5)
= (16000)*1.039766222

=16636.25955

Answer: Hence, the correct option is $16,637.17