Question

1. $100,000 Amortizing Loan

• 9% stated rate

• 20-year amortization

• 5-year balloon

• Annual Payments

a) Calculate annual payment

b) Calculate balloon payment

c) Value at 12% yield

d) Prepare an amortization table

Answer 1

a

Loan amount (PV) =100000

amortization period (n) =20

annual interest rate (i) =9%

Annual payment will be find out by equal annuity formula

equal annuity Payment formula = PV* i *((1+i)^n)/((1+i)^n-1)

100000*9%*((1+9%)^20)/(((1+9%)^20)-1)

=10954.6475

So annual payment will be $10954.65

b.

Balloon payment in 5 year will be loan balance outstanding at 5th year

We will calculate loan balance outstanding by PV of annual payment formula.

Annual payment (P)=10954.6475

annual rate (i) =9%

number of years left after 5 years (n) =20-5 = 15

Loan balance or PV of annual payment formula = P*(1-(1/(1+i)^n))/i

=10954.6475*(1-(1/(1+9%)^15))/9%

=88302.00036

So balloon payment in 5 year would be $88302.00

c

yield rate (i) = 12%

Annual payment (P)= 10954.6475

Balloon payment (FV)=88302.00036

number of years (n) =5

value of loan today =PV of annual payments + PV of balloon payment

=( P*(1-(1/(1+i)^n))/i) + (FV/(1+i)^n)

=(10954.6475*(1-(1/(1+12%)^5))/12%) + (88302.00036/(1+12%)^5)

=89593.97903

So value at 12% yield is $89593.98

d

Amount paid is annual payment amount

Interest = Balance amount before payment * annual interest rate that is 9%

principal portion = Amount paid - interest paid

Principal balance after repayment = Balance before repayment - principal portion repaid

Payment in 5 year = Annual payment + Balloon payment

Loan amortization table
Payment number	Balance before	Amount paid	Interest	Principal portion	Principal balance
	payment
0					100000
1	100,000.00	10954.6475	9,000.00	1,954.65	98,045.35
2	98,045.35	10954.6475	8,824.08	2,130.57	95,914.79
3	95,914.79	10954.6475	8,632.33	2,322.32	93,592.47
4	93,592.47	10954.6475	8,423.32	2,531.33	91,061.14
5	91,061.14	99,256.65	8,195.50	91,061.14	0.00
Total amount paid		143,075.24	43,075.24	100,000.00