Question

Chen deposits $4,622.67 in a bank account paying (566) 8.375% 120 days later, the interest rate changes to i= 11.475% How much money does he have in his bank account exactly 1 year after opening it? (No dates or daycount convention are given, so use theoretical time; i.e. 1 year = 365 days = 52 weeks 12 months etc. and count time in periods.)

a $5,542.67
b. $5,132.10
c. $5.33739
d. $5,388.71
e. $5,491.35

Answer 1

Chen has $9,445.53 in his bank account exactly 1 year after opening it.

Step-by-step explanation:

To calculate the amount of money Chen has in his bank account exactly 1 year after opening it, we need to consider the two different interest rates and the time periods for each rate.

First, let's calculate the amount of money Chen has after 120 days with the initial interest rate of 8.375%. Using the formula for compound interest, we can calculate:

(Amount after 120 days) = (Principal) x (1 + (Rate / 100))^(Time / Number of Periods)

(Amount after 120 days) = $4,622.67 x (1 + 8.375/100)^(120/365) = $4,713.34

Next, we need to calculate the amount of money Chen has after the remaining 245 days with the new interest rate of 11.475%. Again, using the compound interest formula:

(Amount after 245 days) = (Amount after 120 days) x (1 + 11.475/100)^(245/365) = $4,822.86

Finally, to find the total amount after 1 year, we add the interest earned in both periods to the initial deposit:

Total amount = $4,822.86 + $4,622.67 = $9,445.53

Therefore, Chen has $9,445.53 in his bank account exactly 1 year after opening it.