Question

Givens, Hong, and Partners obtained a $7500 term loan at 9.0% compounded annually for new boardroom furniture. Prepare a complete amortization schedule in which the loan is repaid by equal semiannual payments over three years. (Round your answers to the nearest cent. Do not round the intermediate calculations.)

Answer 1

Givens, Hong, and Partners obtained a $7500 term loan at 9.0% compounded annually for new boardroom furniture. Prepare a complete amortization schedule in which the loan is repaid by equal semiannual payments over three years. (Round your answers to the nearest cent. Do not round the intermediate calculations.)

Loan Amount = $7500

Calculating APR with semi-annual compounding from compounded Annually using EAR formula:-

$(1+\frac{r_1}{m_1})^{m_1} = (1+\frac{r_2}{m_2})^{m_2}$

where, r1 = Interest rate compounded annually = 9%

m1 = no of compounding period = 1

r2 = Interest rate compounded annually

m2 = no of compounding period = 2

$(1+\frac{0.09}{1})^{1} = (1+\frac{r_2}{2})^{2}$

Taking 2-root on both sides,

1.04403065 = (1 + r2/2)

r2 = 8.8061%

Calculating the Annual Payment to be paid for Loan:-

$Annual Payments= P*r*\frac{(1+r)^{n}}{(1+r)^{n}-1}$

Where, P = Loan AMount = $7500

r = Periodic Interest rate = 4.40305%

n= no of periods = 3*2 =6

(1 + 0.0440305) Annual Payments = 7500 * 0.0440305 * (1 + 0.0440305)6 – 1

$Annual Payments= 7500*0.0440305*\frac{1.295027877}{1.295027877-1}$

Annual Payments = $1449.54

So, Annual Payments on Loan is $1449.54

- Preparing the AMortization Schedule:-

Year	Beg bal.	Payment	Interest amount	Principal Amount	End Bal.
1	7,500.00	1,449.54	330.23	1,119.31	6,380.69
2	6,380.69	1,449.54	280.94	1,168.60	5,212.09
3	5,212.09	1,449.54	229.49	1,220.05	3,992.04
4	3,992.04	1,449.54	175.77	1,273.77	2,718.28
5	2,718.28	1,449.54	119.69	1,329.85	1,388.42
6	1,388.42	1,449.54	61.13	1,388.41	0.02

Note-

The following Columns are calculated based on:

- Interest amount = beg. Balnace*Monthly interest rate

- Principal maount = Payment - Interest amount

- End Bal. = Beg. Bal + Interest - Payment