a family wants to begin saving for s trip to paris the trip is planned for three years from now and the family wants to accumulate one million shilling for the trip.if twelve deposit are made quartely to an account which earns interest at the rate of 8 percent per year compounded quartely how much should each deposite equsl?how much interest will be earned on their deposit?
To calculate how much each deposit should be, we first need to determine the total number of quarters in three years. Since there are 4 quarters in a year, the total number of quarters in three years is 3 * 4 = 12.
Next, we'll use the compound interest formula to determine the amount of each deposit. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/deposit
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, since the interest is compounded quarterly, the number of times interest is compounded per year (n) is 4, the annual interest rate (r) is 8% in decimal form (0.08), and the number of years (t) is 3.
We want A to be equal to 1,000,000 shillings, so the formula becomes:
1,000,000 = P(1 + 0.08/4)^(4*3)
Now we can solve for P:
P = 1,000,000 / (1 + 0.08/4)^(4*3)
We can evaluate this expression to find the value of P.
To calculate the interest earned on their deposits, we can subtract the total amount of deposits made (12 deposits) from the total future value (1,000,000 shillings) and convert it to shillings.
Once we have solved the equation for P, we can calculate the interest earned on their deposits by subtracting the total amount deposited from the total future value.