Question

Please fill in the blanks (1) ~ (4). Thank you!

On the monthly common payment, Question 1 (Default Points: 1 points) Assume that you borrow 30million JPY from some bank and repay under the plan of total equally payment to pay off at 30 years =360 months later. Calculate the following: Csatisiet (1) <c<|(2) Case 1: If the annual interest rate is 2.4%, the monthly common payment C satisfies Case 2: If the annual interest rate is 3.0%, the monthly common payment C satisfies Caution: Here, (1), (2), (3) and (4) should be integers. (3) (2) X

Answer 1

The formula to be used is the Present value of ordinary annuity formula

ie. PV of loan=Pmt.*(1-(1+r)^-n)/r

where, PV of the loan or borrowings is given as 30 mlns. JPY

Pmt.= the equal monthly payment to be found out---- ??

r= rate of interest, ie.2.4% p.a. ie. 0.20% p.m or 0.002 p.m (for Case 1) &

3% p.a. Ie. 0.25% p.m or 0.0025 p.m (for Case 2)

n= no.of compounding periods= 30 yrs.*12 mths.= 360

So, now, plugging in all the given values in the above formula,

Case 1

ie. PV of loan=Pmt.*(1-(1+r)^-n)/r

30=Pmt.*(1-(1+0.0020)^-360)/0.0020

Mthly. Pmt.=30/((1-(1+0.0020)^-360)/0.0020)

0.116982

Millions

Case 2

30=Pmt.*(1-(1+0.0025)^-360)/0.0025

0.126481

Millions

Answers:

Case 1-- Monthly common payment, C satisfies $116981 < C < $116983

Case 2-- Monthly common payment, C satisfies $ 126480 < C < $ 126482