Question

3. Carolina is considering a purchase of a new warehouse for its expanding parts division. Purchase will be financed with a $4,000,000 loan. The term of the loan: 15 years, amortizing (monthly payments), APR of 4.80%. The first payment is due one month from the day loan is taken. a) What will be the amount of each monthly payment? b) Alternatively, Carolina can use 20-year, monthly amortizing loan with 5.40% APR. How much more in total interest Carolina will pay if it goes with 20-year rather than 15-year loan? (Assume no pre-payments, refinancing, late payments etc.)

Answer 1

Step-1;Calculation of Interest payments over 15 Years term

a.

Monthly Payment

=

Loan amount / Present Value of annuity of 1

=

$          40,00,000.00

/

128.137046

=

$                31,216.58

Working:

Present Value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.004)^-180)/0.004

i

4.80%/12

=

0.004

=

128.137046

n

15*12

=

180

b.

Total Payments over 15 years

=

Monthly Payments x Months in 15 years

=

$                31,216.58

x

180

=

$          56,18,983.93

c.

Total Interest Payment

=

Total Payment over 15 years - Loan Amount

=

$          56,18,983.93

-

$ 40,00,000.00

=

$          16,18,983.93

Step-2:Calculation of Interest payments over 20 Years

a.

Monthly Payment

=

Loan amount / Present Value of annuity of 1

=

$          40,00,000.00

/

146.573495

=

$                27,290.06

Working:

Present Value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.0045)^-240)/0.0045

i

5.40%/12

=

0.0045

=

146.573495

n

20*12

=

240

b.

Total Payments over 15 years

=

Monthly Payments x Months in 15 years

=

$                27,290.06

x

240

=

$          65,49,615.27

c.

Total Interest Payment

=

Total Payment over 15 years - Loan Amount

=

$          65,49,615.27

-

$ 40,00,000.00

=

$          25,49,615.27

Step-3:Calculation of excess Interest payment over 20 years term

Interest Paid over 20 years

$          25,49,615.27

Less:Interest Paymet over 15 years

$          16,18,983.93

Excess Interest Payment made

$             9,30,631.33