Suppose that you just purchased a used car worth $14,000 in today\'s dollars. As

Question

Suppose that you just purchased a used car worth $14,000 in today's dollars. Assume also that, to finance the purchase, you borrowed $12,000 from a local bank at 8% compounded monthly over two years. The bank calculated your monthly payment at $542.36. Assume that average general inflation will run at 1% per month over the next two years. Determine the annual inflation-free interest rate (i') for the bank. What equal monthly payments, in terms of constant dollars over the next two years, are equivalent to the series of actual payments to be made over the life of the loan? A man is planning to retire in 20 years. He can deposit money for his retirement at 8% compounded monthly. It is estimated that the future general inflation (f) until compounded annually. What deposit must be made each month of annual withdrawals of $20.000. in terms first with years following his retirement? (Assume that his occurs al end of the first six months after his retirement.)

Explanation / Answer

Q.4.23

a) Nominal interest rate =8% and inflation rate=1%, then inflation free or real interest rate= (8-1)=7% which is compounded monthly.

Now in decimal 7/100=0.07.

adding 1 to 0.007 we get (1+0.07)=1.07.

Now convert it annual t0 12th power that is (1.07)^12= 2.2521

Substract 1 from it, get (2.2521-1)=1.2521

In % (1.2521*100)=125.21%

Therefore annual inflation free interest rate is 125.21%.

b) Taking 7% componding monthly interest

year 2 end

Total interest =$21108.54

Then loan amount+interest =(12000+$21108.54)=$33108.54.

Therefore monthly payment should be 33108.54/24=$1379.52

Beginning Balance Interest Principal Ending Balance 1 $12,000.00 $1,252.10 $127.42 $11,872.58 2 $11,872.58 $1,238.80 $140.72 $11,731.86 3 $11,731.86 $1,224.12 $155.40 $11,576.46 4 $11,576.46 $1,207.91 $171.61 $11,404.84 5 $11,404.84 $1,190.00 $189.52 $11,215.32 6 $11,215.32 $1,170.23 $209.29 $11,006.02 7 $11,006.02 $1,148.39 $231.13 $10,774.89 8 $10,774.89 $1,124.27 $255.25 $10,519.64 9 $10,519.64 $1,097.64 $281.88 $10,237.75 10 $10,237.75 $1,068.22 $311.30 $9,926.45 11 $9,926.45 $1,035.74 $343.78 $9,582.67 12 $9,582.67 $999.87 $379.65 $9,203.02 year 1 end 13 $9,203.02 $960.26 $419.26 $8,783.76 14 $8,783.76 $916.51 $463.01 $8,320.75 15 $8,320.75 $868.20 $511.32 $7,809.43 16 $7,809.43 $814.85 $564.67 $7,244.75 17 $7,244.75 $755.93 $623.59 $6,621.16 18 $6,621.16 $690.86 $688.66 $5,932.50 19 $5,932.50 $619.01 $760.51 $5,171.99 20 $5,171.99 $539.65 $839.87 $4,332.12 21 $4,332.12 $452.02 $927.50 $3,404.61 22 $3,404.61 $355.24 $1,024.28 $2,380.34 23 $2,380.34 $248.37 $1,131.15 $1,249.18 24 $1,249.18 $130.34 $1,249.18 $0.00

year 2 end

Total interest =$21108.54

Then loan amount+interest =(12000+$21108.54)=$33108.54.

Therefore monthly payment should be 33108.54/24=$1379.52

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