You have just bought an apartment for ¥62 million, using a deposit amounting to ¥8 million,...

You have just bought an apartment for ¥62 million, using a deposit amounting to ¥8 million, and you borrowed the rest. The loan interest rate is 3.2% p.a compounded monthly and you have taken the loan with a twenty year life.

Calculate the monthly repayments needed to fully repay the loan within twenty years (assuming repayments occur at the end of the month).

After 30 months the interest rate increases to 4.2% p.a. what is the new monthly payment needed now to ensure the loan is still paid of within the twenty years?

Solutions

Expert Solution

1. Amount borrowed = 62-8 = 54 million yen

Effective annual interest rate = [1+(3.2/1200)]^12 - 1

= 3.247353% per annum

Now PV = 54 million (or 54,000,000), r = 3.247353%/12 (monthly rate) and n = 20*12 = 240

Thus monthly payment can be computed in excel, using the "pmt" function.

Using the pmt function we get a value of 306,213.21 yen per month.

2. Total principal payment made after 30 months is shown in the table below:

n	PMT	beg bal	int	closing bal
1	306,213.21	54,000,000.00	146,130.89	53,839,917.67
2	306,213.21	53,839,917.67	145,697.68	53,679,402.14
3	306,213.21	53,679,402.14	145,263.31	53,518,452.24
4	306,213.21	53,518,452.24	144,827.76	53,357,066.78
5	306,213.21	53,357,066.78	144,391.03	53,195,244.60
6	306,213.21	53,195,244.60	143,953.11	53,032,984.50
7	306,213.21	53,032,984.50	143,514.02	52,870,285.31
8	306,213.21	52,870,285.31	143,073.73	52,707,145.83
9	306,213.21	52,707,145.83	142,632.26	52,543,564.88
10	306,213.21	52,543,564.88	142,189.59	52,379,541.25
11	306,213.21	52,379,541.25	141,745.72	52,215,073.76
12	306,213.21	52,215,073.76	141,300.65	52,050,161.19
13	306,213.21	52,050,161.19	140,854.37	51,884,802.36
14	306,213.21	51,884,802.36	140,406.89	51,718,996.04
15	306,213.21	51,718,996.04	139,958.20	51,552,741.02
16	306,213.21	51,552,741.02	139,508.29	51,386,036.10
17	306,213.21	51,386,036.10	139,057.17	51,218,880.06
18	306,213.21	51,218,880.06	138,604.82	51,051,271.66
19	306,213.21	51,051,271.66	138,151.25	50,883,209.70
20	306,213.21	50,883,209.70	137,696.45	50,714,692.95
21	306,213.21	50,714,692.95	137,240.43	50,545,720.16
22	306,213.21	50,545,720.16	136,783.16	50,376,290.11
23	306,213.21	50,376,290.11	136,324.66	50,206,401.57
24	306,213.21	50,206,401.57	135,864.92	50,036,053.28
25	306,213.21	50,036,053.28	135,403.94	49,865,244.01
26	306,213.21	49,865,244.01	134,941.71	49,693,972.50
27	306,213.21	49,693,972.50	134,478.23	49,522,237.52
28	306,213.21	49,522,237.52	134,013.49	49,350,037.80
29	306,213.21	49,350,037.80	133,547.49	49,177,372.08
30	306,213.21	49,177,372.08	133,080.24	49,004,239.11

Thus principal amount due after 30 months = 49,004,239.11 yen or 49.0042 million yen

Now new interest rate = 4.2% and as this is also compunded monthly then effective rate =

[1+(4.2/1200)]^12 - 1 = 4.28180072%

Thus balance time left = 240 months - 30 months = 210 months

Again we will use the pmt function with PV = 49,004,239.11, r = 4.28180072%/12 and n = 210

We get a monthly payment of 331,996.01 yen in this case.

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

. You just won 100 million playing the lottery yesterday and you deposit 50 million in...

. You just won 100 million playing the lottery yesterday and you deposit 50 million in the local bank. Would you spending habits and the way you think about and select goods and service change compared to the way it was before you won lottery? what types of goods would you buy and in what quantities? why? Please explain it by some economic concept as much detail as possible. Please being organize

1. You just won 100 million playing the lottery yesterday and you deposit 50 million in...

1. You just won 100 million playing the lottery yesterday and you deposit 50 million in the local bank. Would you spending habits and the way you think about and select goods and service change compared to the way it was before you won lottery? what types of goods would you buy and in what quantities? why? Please explain it by some economic concept as much detail as possible.

You have just bought a house and have taken out a mortgage (an installment) loan for...

You have just bought a house and have taken out a mortgage (an installment) loan for $500,000. This is a 30-year loan that requires monthly payments and the first payment is due one month from today. The APR for the loan is 24%. You are interested to know how much of your 210th monthly payment will go toward the repayment of principal? That amount is _______________ Question 10 options: $762.65 $9,586.98 $625.64 $9,494.78 $513.24 $9,382.38 $421.04 $9,245.37

You have just started to deposit $250 at the end of each month into a bank...

You have just started to deposit $250 at the end of each month into a bank account. The bank manager states that you can receive $20,000 after 6 years from that account, if there is no transaction other than monthly deposits. What is interest rate provided by the bank for this account?

you just bought a house and have a $188,000 mortgage. the mortgage is for 15 years...

you just bought a house and have a $188,000 mortgage. the mortgage is for 15 years and has a nominal rate of 4.25%.on the 24th payment what will be the amount going to principal?

You have just bought a house and have a $125,000, 25-year mortgage with a fixed interest...

You have just bought a house and have a $125,000, 25-year mortgage with a fixed interest rate of 8.5 percent with monthly payments. Over the next five years, what percentage of your mortgage payments will go toward the repayment of principal?.

3) You just bought a house for $200,000. You have agreed to make 5 payments at...

3) You just bought a house for $200,000. You have agreed to make 5 payments at the end of the year for 5 years with an interest rate of 6%. What will the annual payment be? Create a loan amortization schedule. beginning balance payment interest principal ending balance 1 2 3 4 5

If you deposit $1,600 into an account paying 8% compunded monthly, how much will you have...

If you deposit $1,600 into an account paying 8% compunded monthly, how much will you have in 4 years?

You have just received notification that you have won the $2.04 million first prize in the...

You have just received notification that you have won the $2.04 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 82 years from now. What is the present value of your windfall if the appropriate discount rate is 8 percent?

You have just received notification that you have won the $1 million first prize in the...

You have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 8.45 percent? (Do not round intermediate calculations and enter your answer in dollars, not millons of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.)

Subjects