Question
4.79. Kathy Stonewall bought a new car for $15,458. A dealer's financing was available through a local bank at an interest rate of 11.5% compounded monthly. Dealer financing required a 10% down payment and 60 equal monthly payments. Because d the interest rate was rather high, Kathy checked her credit union for possible financing. The loan officer at the credit union quoted a 9.8% interest rate for a new-car loan and 10.5% for a used car. But to be r eligible for the loan, Kathy has to be a member of g the union for at least six months. Since she joined the union two months ago, she has to wait four more
Explanation / Answer
Car price is $15458
10% is the down payment required, so total loan principle = 15458 * 90% = 13912.2
Lets calculate what would be the monthly payment for loan taken from dealer.
This can be calculated in an excel as follows
Monthly Payment to dealer =PMT((11.5/12)%,60,-13912.2,0,0) = $305.97
Cash flows schedule is as follows
Now lets suppose after 4 months, loan is financed thru credit union.
Principle left = $13,211.65
Monthly Payment to credit union =PMT((10.5/12)%,56,-13211.65,0,0) = $299.44
Here only 56 months are remaining.
Cash flow schedule changes as follows
Total interest payments = $4,080.04
Interest paid to dealer in 4 months = $523.31
Interest paid to credit union in 56 months = $3,556.73
Month EMI Interest Paid Principle Paid Principle Left 0 $13,912.20 1 $305.97 $133.33 $172.64 $13,739.56 2 $305.97 $131.67 $174.29 $13,565.26 3 $305.97 $130.00 $175.97 $13,389.30 4 $305.97 $128.31 $177.65 $13,211.65 5 $305.97 $126.61 $179.35 $13,032.29 6 $305.97 $124.89 $181.07 $12,851.22 7 $305.97 $123.16 $182.81 $12,668.41 8 $305.97 $121.41 $184.56 $12,483.85 9 $305.97 $119.64 $186.33 $12,297.53 10 $305.97 $117.85 $188.11 $12,109.41 11 $305.97 $116.05 $189.92 $11,919.49 12 $305.97 $114.23 $191.74 $11,727.76 13 $305.97 $112.39 $193.57 $11,534.18 14 $305.97 $110.54 $195.43 $11,338.75 15 $305.97 $108.66 $197.30 $11,141.45 16 $305.97 $106.77 $199.19 $10,942.26 17 $305.97 $104.86 $201.10 $10,741.15 18 $305.97 $102.94 $203.03 $10,538.13 19 $305.97 $100.99 $204.98 $10,333.15 20 $305.97 $99.03 $206.94 $10,126.21 21 $305.97 $97.04 $208.92 $9,917.29 22 $305.97 $95.04 $210.92 $9,706.36 23 $305.97 $93.02 $212.95 $9,493.42 24 $305.97 $90.98 $214.99 $9,278.43 25 $305.97 $88.92 $217.05 $9,061.38 26 $305.97 $86.84 $219.13 $8,842.25 27 $305.97 $84.74 $221.23 $8,621.03 28 $305.97 $82.62 $223.35 $8,397.68 29 $305.97 $80.48 $225.49 $8,172.19 30 $305.97 $78.32 $227.65 $7,944.54 31 $305.97 $76.14 $229.83 $7,714.71 32 $305.97 $73.93 $232.03 $7,482.68 33 $305.97 $71.71 $234.26 $7,248.42 34 $305.97 $69.46 $236.50 $7,011.92 35 $305.97 $67.20 $238.77 $6,773.15 36 $305.97 $64.91 $241.06 $6,532.10 37 $305.97 $62.60 $243.37 $6,288.73 38 $305.97 $60.27 $245.70 $6,043.03 39 $305.97 $57.91 $248.05 $5,794.98 40 $305.97 $55.54 $250.43 $5,544.55 41 $305.97 $53.14 $252.83 $5,291.72 42 $305.97 $50.71 $255.25 $5,036.47 43 $305.97 $48.27 $257.70 $4,778.77 44 $305.97 $45.80 $260.17 $4,518.60 45 $305.97 $43.30 $262.66 $4,255.94 46 $305.97 $40.79 $265.18 $3,990.76 47 $305.97 $38.24 $267.72 $3,723.04 48 $305.97 $35.68 $270.29 $3,452.75 49 $305.97 $33.09 $272.88 $3,179.87 50 $305.97 $30.47 $275.49 $2,904.38 51 $305.97 $27.83 $278.13 $2,626.25 52 $305.97 $25.17 $280.80 $2,345.45 53 $305.97 $22.48 $283.49 $2,061.96 54 $305.97 $19.76 $286.21 $1,775.76 55 $305.97 $17.02 $288.95 $1,486.81 56 $305.97 $14.25 $291.72 $1,195.09 57 $305.97 $11.45 $294.51 $900.58 58 $305.97 $8.63 $297.33 $603.25 59 $305.97 $5.78 $300.18 $303.06 60 $305.97 $2.90 $303.06 $0.00 Total $18,357.93 $4,445.73
