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Answer 1-a Answer 2-a Calculation of total cost of new car We can use the present value of annuity formula to calculate the present value. Total cost of new car = Down payment + Finance amount Present value of annuity = P x {[1 - (1+r)^-n]/r} Down payment = $5000 Present Value of annuity = ? P = annuity = $400 Calculation of finance amount r = interest rate = 8% We can use the present value of annuity formula to calculate the Finance amount n = number of years = 14 Present value of annuity = P x {[1 - (1+r)^-n]/r} Present value of annuity = 400 x {[1 - (1+0.08)^-14]/0.08} Present Value of annuity = finance amount = ? Present value of annuity = 400 x 8.244237 P = Loan monthly payment = $400 Present value of annuity = 3297.69 r = interest rate per month = 11%/12 = 0.009167 Present Value of ordinary annuity = $3,297.69 n = number of months loan payment = 48 Present value of annuity = 400 x {[1 - (1+0.009167)^-48]/0.009167} Answer 2-b Present value of annuity = 400 x 38.69142 We can use the present value of annuity formula to calculate the present value. Present value of annuity = 15476.57 Present value of annuity = P x {[1 - (1+r)^-n]/r} Finance amount = $15,476.57 Present Value of annuity = ? P = annuity = $200 Total cost of new car = $5000 + $15,476.57 r = interest rate = 4% Total cost of new car = $20,476.57 n = number of years = 7 You can afford car costing $20,476.57 if you finance it for 48 months. Present value of annuity = 200 x {[1 - (1+0.04)^-7]/0.04} Present value of annuity = 200 x 6.002055 Answer 1-b Present value of annuity = 1200.41 Calculation of total cost of new car Present Value of ordinary annuity = $1,200.41 Total cost of new car = Down payment + Finance amount Down payment = $5000 Answer 2-c We can use the present value of annuity formula to calculate the present value. Calculation of finance amount Present value of annuity = P x {[1 - (1+r)^-n]/r} We can use the present value of annuity formula to calculate the Finance amount Present Value of annuity = ? Present value of annuity = P x {[1 - (1+r)^-n]/r} P = annuity = $700 Present Value of annuity = finance amount = ? r = interest rate = 0% P = Loan monthly payment = $400 n = number of years = 8 r = interest rate per month = 11%/12 = 0.009167 Present value of annuity = 700 x {[1 - (1+0.00)^-8]/0.00} n = number of months loan payment = 60 Present value of annuity = 700 x 0 Present value of annuity = 400 x {[1 - (1+0.009167)^-60]/0.009167} Present value of annuity = 700 Present value of annuity = 400 x 45.99303 Present Value of ordinary annuity = $700 Present value of annuity = 18,397.21 Finance amount = $18,397.21 Total cost of new car = $5000 + $18,397.21 Total cost of new car = $23,397.21 You can afford car costing $23,397.21 if you finance it for 60 months.
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