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?
did this for you yesterday
http://www.jiskha.com/display.cgi?id=1447865841
Thanks Reiny
To calculate how much each deposit should be, we need to use the formula for the future value of an investment with regular deposits, compounded quarterly:
FV = P * (1 + r/n)^(nt) + PMT * ((1 + r/n)^(nt) - 1) / (r/n)
Where:
FV = Future Value (1,000,000 shillings in this case)
P = Principal Amount (the initial deposit, which we need to find)
r = Annual interest rate (8%)
n = Number of times interest is compounded per year (4 for quarterly)
t = Number of years (3 years in this case)
PMT = Amount of the regular deposits
Substituting the values into the formula, we have:
1,000,000 = P * (1 + 0.08/4)^(4*3) + PMT * ((1 + 0.08/4)^(4*3) - 1) / (0.08/4)
Simplifying the equation step by step:
1,000,000 = P * (1 + 0.02)^(12) + PMT * ((1 + 0.02)^(12) - 1) / 0.02
1,000,000 = P * 1.268241 + PMT * 1.268241 / 0.02
1,000,000 = P * 1.268241 + PMT * 63.41205
Now we have two variables, P and PMT. To solve for them, we need a second equation. Since we have the information that twelve deposits are made quarterly, we can use this to find the value of PMT.
PMT = Total amount to be accumulated / Number of deposits
PMT = 1,000,000 / 12
PMT = 83,333.33 shillings (rounded to two decimal places)
Now, substituting this value back into the equation, we can solve for P:
1,000,000 = P * 1.268241 + 83,333.33 * 63.41205
1,000,000 - 83,333.33 * 63.41205 = P * 1.268241
1,000,000 - 5,280,110.26 = P * 1.268241
-4,280,110.26 = P * 1.268241
P = -4,280,110.26 / 1.268241
P = -3,376,966.65
Since a negative principal amount doesn't make sense in this context, it appears there may be an error in the problem statement or calculations. Please double-check the given values and equations to ensure accuracy.
Regarding the interest earned on the deposits, to calculate it, we subtract the total amount accumulated (1,000,000 shillings) from the sum of the actual deposits made:
Interest Earned = (Total Amount Accumulated) - (Sum of Actual Deposits)
Since each deposit is the same amount (83,333.33 shillings), we can calculate the sum of the actual deposits as:
Sum of Actual Deposits = Number of Deposits * Amount of Each Deposit
Sum of Actual Deposits = 12 * 83,333.33
Sum of Actual Deposits = 999,999.96 shillings
Therefore, the interest earned on their deposits would be:
Interest Earned = 1,000,000 - 999,999.96
Interest Earned = 0.04 shillings (rounded to two decimal places)
Please note that due to rounding and the assumption of continuous regular deposits, there may be slight discrepancies in the final results.