A man borrows 120,000 naira from a bank to buy a computer at 8% compound interest per annum. If he repays 7000 naira every six months, work out the amount he still owes at the end of 2½years
To find the amount the man still owes at the end of 2½ years, we first need to determine the number of compounding periods.
Since he is repaying every six months, and there are 2 compounding periods within a year, the total number of periods over 2½ years would be:
2.5 years x 2 periods/year = 5 periods
Now we can calculate the outstanding balance using compound interest formula.
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (including interest)
P is the principal amount (the initial loan amount)
r is the annual interest rate (in decimal form)
n is the number of compounding periods per year (in this case, 2)
t is the time in years
In this case:
P = ₦120,000
r = 8% = 0.08
n = 2
t = 2.5 years
Using the compound interest formula, we can calculate the final amount (A).
A = ₦120,000(1 + 0.08/2)^(2*2.5)
A = ₦120,000(1.04)^(5)
A ≈ ₦140,320.59
The final amount after 2.5 years including interest is approximately ₦140,320.59.
To find out how much he still owes, we subtract the repayments made over the 2.5 years.
Total repayments made = 7000 naira/6 months x 5 periods = ₦35,000
Amount still owed = ₦140,320.59 - ₦35,000 = ₦105,320.59
Therefore, the man still owes approximately ₦105,320.59 at the end of 2½ years.
To work out the amount that the man still owes at the end of 2½ years, we need to calculate the total amount that the man will repay in 2½ years and then subtract that from the original amount he borrowed.
First, let's calculate the total repayment in 2½ years.
There are 2 repayment periods per year (every 6 months), so in 2½ years, there will be a total of 2½ * 2 = 5 repayment periods.
The man repays 7000 naira every 6 months, so in 2½ years, he will repay a total of 5 * 7000 = 35,000 naira.
Now, let's calculate the amount that he still owes.
The loan amount is 120,000 naira, and we need to deduct the total repayment amount of 35,000 naira.
120,000 - 35,000 = 85,000 naira
Therefore, the man still owes 85,000 naira at the end of 2½ years.
To find the amount he still owes at the end of 2 1/2 years, we need to calculate the compound interest on the loan and subtract the amount he has already repaid.
First, we need to calculate the compound interest after 2 1/2 years. The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan
P = the initial principal (loan amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the loan amount (P) is 120,000 naira, the annual interest rate (r) is 8% or 0.08, the number of compounding periods per year (n) is 1 (since they are making semi-annual payments), and the number of years (t) is 2 1/2 or 2.5.
Using the compound interest formula, we can calculate the future value of the loan after 2 1/2 years:
A = 120,000(1 + 0.08/1)^(1*2.5)
A = 120,000(1.08)^(2.5)
A ≈ 143,488.69
Next, we need to subtract the amount he has repaid from the future value of the loan:
Remaining loan amount = A - (7000 x 5)
Remaining loan amount = 143,488.69 - 35,000
Remaining loan amount = 108,488.69
Therefore, the man still owes approximately 108,488.69 naira at the end of 2 1/2 years.