A family wants to begin saviving for a trip to paris. The trip is planned for 3 years from now, and the family wants to accumulate one million shillings for the trip, if twelve deposits are made quartely to an account which earns interest at the rate of 8 percent per year compounded quartely, how much should each deposit equal?, How much interest will be earned on their deposits

To calculate the amount of each deposit, we need to use the future value formula for compound interest. The formula is:

FV = P * (1 + r/n)^(nt)

Where:
FV = Future Value (desired amount: 1 million shillings)
P = Principal amount (deposit amount)
r = Annual interest rate (8 percent)
n = Number of times interest is compounded per year (4 for quarterly)
t = Number of years (3)

Let's calculate the deposit amount (P):

1 million = P * (1 + 0.08/4)^(4*3)

To solve for P, we'll divide both sides by the right-hand side:

1,000,000 / (1.02^12) = P

Now we need to compute 1.02^12:

1.02^12 ≈ 1.26824

Dividing 1 million by 1.26824 gives us:

P ≈ 1,000,000 / 1.26824 ≈ 788,610 shillings

Therefore, each deposit should amount to approximately 788,610 shillings.

To calculate the total interest earned on the family's deposits, we can subtract the total amount saved from the principal amount. The total amount saved can be found by multiplying the deposit amount by the number of deposits made over the 3-year period.

Total amount saved = P * 12 * 3

Total interest earned = (Total amount saved - Principal amount)

Plugging in the values:

Total amount saved = 788,610 * 12 * 3 ≈ 28,351,960 shillings

Total interest earned = (28,351,960 - 788,610) ≈ 27,563,350 shillings

Therefore, the family will earn approximately 27,563,350 shillings in interest on their deposits.