at the beginning of the 1974/1975 year,a man invented 2,000 naira a bank at 12 and half percentage compound interest.if he redraws 650 naira at the end of each school year after payment of interest from the money he his son's school fees.how much did he have left at the beginning of 1978/1979
Well, that's quite a math problem you have there! Let me put on my clown goggles and calculate it for you.
If the man invested 2,000 naira at 12 and a half percent compound interest, we need to break it down into school years. Each year, he redraws 650 naira for his son's school fees.
First, let's figure out how much interest he earned each year. 12 and a half percent of 2,000 naira is 250 naira. So, after subtracting the interest, he would have 2,000 - 250 = 1,750 naira at the end of the first year.
After the first year, he would withdraw 650 naira for school fees, leaving him with 1,750 - 650 = 1,100 naira. Then, the same process repeats for the next two years.
Each year, the man would earn interest on the remaining balance. So, in the second year, he would earn 12 and a half percent interest on 1,100 naira, which is 137.5 naira. After withdrawing 650 naira for school fees, he would have 1,100 + 137.5 - 650 = 587.5 naira left.
In the third year, he would earn interest on 587.5 naira, which amounts to 73.44 naira. After withdrawing 650 naira, he would have 587.5 + 73.44 - 650 = 10.94 naira left.
Now, we can calculate how much he would have left at the beginning of the 1978/1979 year. Adding up all the remaining amounts, he would have 1,750 + 587.5 + 10.94 = 2,348.44 naira.
So, after all the calculations, he would have approximately 2,348.44 naira left at the beginning of the 1978/1979 year. Just enough for a clown wig and some clown shoes!
To calculate the amount the man had left at the beginning of the 1978/1979 year, we need to determine the growth of the money over the four-year period.
Step 1: Calculate the annual interest earned
At a compound interest rate of 12.5%, the man would earn an annual interest of (12.5/100) * 2000 = ₦250 per year.
Step 2: Calculate the amount of money withdrawn each year
The man withdrew ₦650 at the end of each school year after paying the interest. Since there are four school years in the given timeframe, the total amount withdrawn is ₦650 * 4 = ₦2600.
Step 3: Calculate the growth of the money over the four-year period
Using the compound interest formula A = P(1 + r/n)^(nt), where:
A = total amount
P = principal amount (initial amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
For the given scenario:
P = ₦2000
r = 12.5/100 = 0.125
n = 1 (interest compounded annually)
t = 4 years
A = 2000(1 + 0.125/1)^(1*4)
A = 2000(1.125)^4
A ≈ ₦3546.88
Step 4: Calculate the final amount after subtracting the withdrawals
The man had ₦3546.88 at the end of the four-year period, but he withdrew ₦2600. Therefore, the amount left at the beginning of 1978/1979 would be ₦3546.88 - ₦2600 = ₦946.88.
Therefore, the man had ₦946.88 left at the beginning of the 1978/1979 year.
To calculate how much money the man had left at the beginning of the 1978/1979 year, we need to calculate the compound interest for four years (from 1974/1975 to 1978/1979), subtract the annual withdrawals, and finally add the remaining principal amount.
Here's the step-by-step explanation of how to calculate it:
Step 1: Calculate the compound interest for four years.
To calculate compound interest, we use the formula: A = P(1 + (r/n))^(nt)
Where:
A = Total amount after interest
P = Principal amount (in this case, 2,000 naira)
r = Annual interest rate (12.5% = 0.125)
n = Number of times interest is compounded per year (annually)
t = Number of years
In this case, r = 0.125, n = 1 (compounded annually), and t = 4 (four years).
A = 2,000(1 + (0.125/1))^(1*4)
A = 2,000(1 + 0.125)^4
A = 2,000(1.125)^4
A ≈ 2,000(1.598)
A ≈ 3,196 naira (rounded to the nearest whole naira)
Step 2: Calculate the total amount withdrawn over four years.
The man withdrew 650 naira at the end of each school year. So, to calculate the total amount withdrawn over four years, multiply the annual withdrawal by the number of years.
Total amount withdrawn = 650 * 4 = 2,600 naira
Step 3: Calculate the remaining principal amount.
To get the remaining principal amount at the beginning of the 1978/1979 year, subtract the total amount withdrawn from the total amount after interest.
Remaining principal amount = Total amount after interest - Total amount withdrawn
Remaining principal amount = 3,196 - 2,600
Remaining principal amount = 596 naira
Therefore, the man had 596 naira left at the beginning of the 1978/1979 year.