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標題:
Compounded interest loan
發問:
kaitlin borrows $4000 to buy a new computer. At the end of each quarter (3 months), and after interest for the quarter has been added at the rate of 3% of the unpaid balance, she makes a repayment of $500.(a)how many repayments must be made?(b)how much is the final repayment?(c)what is the total of the... 顯示更多 kaitlin borrows $4000 to buy a new computer. At the end of each quarter (3 months), and after interest for the quarter has been added at the rate of 3% of the unpaid balance, she makes a repayment of $500. (a)how many repayments must be made? (b)how much is the final repayment? (c)what is the total of the repayments? (d)if instead she had wanted to spread the regular repayments over four years, how much would she need to pay each quarter and what would be the total of the repayments to the nearest dollar? Please show all workings thx =)!
Part (a) 4,000=500/(1+3%)+500/(1+3%)^2+500/(1+3%)^3+..... 4000=500 [1/1.03+1/(1.03)^2+1/(1.03)^3+1/(1.03)^4+....1/(1.03)^n] 8= [1/(1.03)+1/(1.03)^2+.....1/(1.03)^n] 8=(1/1.03)[1-(1/1.03)^n]/(1-1/1.03) 8=(1/1.03)[1-(1/1.03)^n]/(0.03/1.03) 8=[1-(1/1.03)^n]/0.03 0.24=1-(1/1.03)^n (1/1.03)^n=0.76 nlog(1/1.03)=log0.76 n=log0.76/log(1/1.03) =9.28 so 10 repayments must be made. Part (b) 4000=500/(1+3%)+500/(1+3%)^2+500/(1+3%)^3+...500/(1+3%)^9+R/(1+3%)^10 4000=(500/1.03)[1-(1/1.03)^9]/(1-1/1.03)+R/(1.03)^10 4000=500[1-(1/1.03)^9]/0.03+R/(1.03)^10 4000=3893.05+R/1.03^10 106.95=R/1.03^10 R=143.73 The final repayment is 143.73 Part (c) The total repayment =500*9+143.73 =4643.73 Part (d) 4000=R/(1.03)+R/(1.03)^2+R/(1.03)^3+....R/1.03^16 4000=R{1/1.03[1-(1/1.03)^16]/(1-1/1.03) 4000=R[1-(1/1.03)^16]/0.03 4000=12.5611R R=318.44 The total repayment=318.44*16=5095.04
其他解答:1C924F1C0172E337
Compounded interest loan
發問:
kaitlin borrows $4000 to buy a new computer. At the end of each quarter (3 months), and after interest for the quarter has been added at the rate of 3% of the unpaid balance, she makes a repayment of $500.(a)how many repayments must be made?(b)how much is the final repayment?(c)what is the total of the... 顯示更多 kaitlin borrows $4000 to buy a new computer. At the end of each quarter (3 months), and after interest for the quarter has been added at the rate of 3% of the unpaid balance, she makes a repayment of $500. (a)how many repayments must be made? (b)how much is the final repayment? (c)what is the total of the repayments? (d)if instead she had wanted to spread the regular repayments over four years, how much would she need to pay each quarter and what would be the total of the repayments to the nearest dollar? Please show all workings thx =)!
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最佳解答:Part (a) 4,000=500/(1+3%)+500/(1+3%)^2+500/(1+3%)^3+..... 4000=500 [1/1.03+1/(1.03)^2+1/(1.03)^3+1/(1.03)^4+....1/(1.03)^n] 8= [1/(1.03)+1/(1.03)^2+.....1/(1.03)^n] 8=(1/1.03)[1-(1/1.03)^n]/(1-1/1.03) 8=(1/1.03)[1-(1/1.03)^n]/(0.03/1.03) 8=[1-(1/1.03)^n]/0.03 0.24=1-(1/1.03)^n (1/1.03)^n=0.76 nlog(1/1.03)=log0.76 n=log0.76/log(1/1.03) =9.28 so 10 repayments must be made. Part (b) 4000=500/(1+3%)+500/(1+3%)^2+500/(1+3%)^3+...500/(1+3%)^9+R/(1+3%)^10 4000=(500/1.03)[1-(1/1.03)^9]/(1-1/1.03)+R/(1.03)^10 4000=500[1-(1/1.03)^9]/0.03+R/(1.03)^10 4000=3893.05+R/1.03^10 106.95=R/1.03^10 R=143.73 The final repayment is 143.73 Part (c) The total repayment =500*9+143.73 =4643.73 Part (d) 4000=R/(1.03)+R/(1.03)^2+R/(1.03)^3+....R/1.03^16 4000=R{1/1.03[1-(1/1.03)^16]/(1-1/1.03) 4000=R[1-(1/1.03)^16]/0.03 4000=12.5611R R=318.44 The total repayment=318.44*16=5095.04
其他解答:1C924F1C0172E337
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