Question

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.

Answer 1

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