In: Economics
4. Ms. Klein borrowed $10,000 from a bank on annuity
for 2 years at 20% annual interest compounded and payable
semiannually (every six months). Calculate the semiannual payments
and provide a table that shows semiannual payment, balance,
interest payment, payment to principal for each payment. Also
calculate the total amount which Ms. Klein will pay to the bank for
the borrowed amount including interest and principal payments in
the entire period of two years.
We are given the following information:
Payment | PMT | To be calculated |
Rate of interest | r | 20.00% |
Number of years | n | 2.00 |
Semi Annual | frequency | 2.00 |
Loan amount | PV | 10000.00 |
We need to solve the following equation to arrive at the required PMT:
So the PMT is $3154.71
Below is the amortization schedule:
Period | Opening Balance | PMT | Interest | Principal repayment | Closing Balance |
1 | $ 10,000.00 | $ 3,154.71 | $ 1,000.00 | $ 2,154.71 | $ 7,845.29 |
2 | $ 7,845.29 | $ 3,154.71 | $ 784.53 | $ 2,370.18 | $ 5,475.11 |
3 | $ 5,475.11 | $ 3,154.71 | $ 547.51 | $ 2,607.20 | $ 2,867.92 |
4 | $ 2,867.92 | $ 3,154.71 | $ 286.79 | $ 2,867.92 | $ 0.00 |
Total | $ 12,618.83 | $ 2,618.83 | $ 10,000.00 |
Opening balance = previous year's closing balance
Closing balance = Opening balance-Principal repayment
PMT is calculated as per the above formula
Interest = 0.2 /2 x opening balance
Principal repayment = PMT - Interest
So total amount she has to pay is $12,618.83 including
principal and interest