I need help on this short problem set, which is attached below. Thank you

Name______________________4-Digit #______________Section________ Present and Future Values: [153380Q4092115] Mayhem has agreed to make eight quarterly $30,000 payments into an account starting today. The last payment will be twenty-one months from today. If the interest rate is 12% with quarterly compounding on the payment dates, to what value will the account balance grow at the time of the last quarterly payment into the account? $___________ In the previous situation, to what value will the account balance grow one year after the last payment has been made [assuming quarterly compounding continues] ? $___________ Trojan just bought a new car for $70,000 paying $30,000 down. Orange has agreed to make twelve quarterly payments starting one year and three months after the car's purchase date. The lender agreed to this delayed payment plan only when Orange agreed to the accrual on interest during the 'payment holiday'. The interest rate on this loan is 10%. What will be carrying value on this loan after the 4th payment has been made? $_________ Hint: the carrying value of a note equals the present value of the remaining payments while using the same (original) rate of interest. Without influencing your work for the previous requirement, assume Orange refinanced the carrying value of the loan after the eighth payment had been made. [This means the carrying value after the eighth payment is 'paid off' with a new loan in the same amount but at a lower interest rate than the former note.] The new interest rate was 8%. What size will be the last 4 payments required to pay off this loan after the refinancing? $__________ Merlin has found that it will need $3,000,000 three years from today's date. What equal semi-annual payments starting today will Merlin have to pay into an account earning 6% per year [with semi-annual compounding] in order to accomplish this goal? The last payment into the account will be made three years from today. How large will each of these payments need to be for Merlin to accomplish this goal? $_________ quarter quarter 1 2 3 4 5 6 7 8 9 10 11 12 question 1 question 2 30000.00 60900.00 92727.00 125508.81 159274.07 194052.30 229873.87 266770.08 274773.18 283016.38 291506.87 300252.08 installment 0 1 2 3 4 5 6 39152 79,478.56 121,014.92 163,797.36 207,863.29 253,251.18 300,000.72 question 5 question 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 41,000.00 42,025.00 43,075.63 44,152.52 40,952.03 at this point the first payment is made 37,671.53 34,309.02 30,862.44 at this point the fourth payment is made 27,329.70 23,708.65 19,997.06 16,192.69 at this point the eight payment is made 12,293.21 8,296.24 4,199.34 0.03 12263.9531 question 4 8256.64215 4169.18499 -0.02130976 Name______________________4-Digit #______________Section________ Present and Future Values: [153380Q4092115] 1) Mayhem has agreed to make eight quarterly $30,000 payments into an account starting today. The last payment will be twenty-one months from today. If the interest rate is 12% with quarterly compounding on the payment dates, to what value will the account balance grow at the time of the last quarterly payment into the account? $___________ Answer = $266,770 [30000+ (30000*[(1.03 7-1)/.03]*1.03)]] 2) In the previous situation, to what value will the account balance grow one year after the last payment has been made [assuming quarterly compounding continues] ? $___________ Answer = $300,252 [266770*(1.03) 4] 3) Trojan just bought a new car for $70,000 paying $30,000 down. Orange has agreed to make twelve quarterly payments starting one year and three months after the car's purchase date. The lender agreed to this delayed payment plan only when Orange agreed to the accrual on interest during the 'payment holiday'. The interest rate on this loan is 10%. What will be carrying value on this loan after the 4th payment has been made? $_________ Hint: the carrying value of a note equals the present value of the remaining payments while using the same (original) rate of interest. Answer = $30,862.44 [Installment amount*PVIFA (2.5%, 8); Where installment amount = (40000*1.025 5) / (1+ PVIFA (2.5%, 11))] 4) Without influencing your work for the previous requirement, assume Orange refinanced the carrying value of the loan after the eighth payment had been made. [This means the carrying value after the eighth payment is 'paid off' with a new loan in the same amount but at a lower interest rate than the former note.] The new interest rate was 8%. What size will be the last 4 payments required to pay off this loan after the refinancing? $__________ Answer = 4252.59 [Carrying amount of loan after 8th payment / PVIFA (2%, 4); Where carrying amount of loan after 8th payment = installment amount computed earlier * PVIFA (2.5%, 4) 5) Merlin has found that it will need $3,000,000 three years from today's date. What equal semi-annual payments starting today will Merlin have to pay into an account earning 6% per year [with semi-annual compounding] in order to accomplish this goal? The last payment into the account will be made three years from today. How large will each of these payments need to be for Merlin to accomplish this goal? $_________ Answer = $39,152 quarter quarter 1 2 3 4 5 6 7 8 9 10 11 12 question 1 question 2 30000.00 60900.00 92727.00 125508.81 159274.07 194052.30 229873.87 266770.08 274773.18 283016.38 291506.87 300252.08 installment 0 1 2 3 4 5 6 39152 79,478.56 121,014.92 163,797.36 207,863.29 253,251.18 300,000.72 question 5 question 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 41,000.00 42,025.00 43,075.63 44,152.52 40,952.03 at this point the first payment is made 37,671.53 34,309.02 30,862.44 at this point the fourth payment is made 27,329.70 23,708.65 19,997.06 16,192.69 at this point the eight payment is made 12,293.21 8,296.24 4,199.34 0.03 12263.9531 question 4 8256.64215 4169.18499 -0.02130976 Name______________________4-Digit #______________Section________ Present and Future Values: [153380Q4092115] 1) Mayhem has agreed to make eight quarterly $30,000 payments into an account starting today. The last payment will be twenty-one months from today. If the interest rate is 12% with quarterly compounding on the payment dates, to what value will the account balance grow at the time of the last quarterly payment into the account? $___________ Answer = $266,770 [30000+ (30000*[(1.03 7-1)/.03]*1.03)]] 2) In the previous situation, to what value will the account balance grow one year after the last payment has been made [assuming quarterly compounding continues] ? $___________ Answer = $300,252 [266770*(1.03) 4] 3) Trojan just bought a new car for $70,000 paying $30,000 down. Orange has agreed to make twelve quarterly payments starting one year and three months after the car's purchase date. The lender agreed to this delayed payment plan only when Orange agreed to the accrual on interest during the 'payment holiday'. The interest rate on this loan is 10%. What will be carrying value on this loan after the 4th payment has been made? $_________ Hint: the carrying value of a note equals the present value of the remaining payments while using the same (original) rate of interest. Answer = $30,862.44 [Installment amount*PVIFA (2.5%, 8); Where installment amount = (40000*1.025 5) / (1+ PVIFA (2.5%, 11))] 4) Without influencing your work for the previous requirement, assume Orange refinanced the carrying value of the loan after the eighth payment had been made. [This means the carrying value after the eighth payment is 'paid off' with a new loan in the same amount but at a lower interest rate than the former note.] The new interest rate was 8%. What size will be the last 4 payments required to pay off this loan after the refinancing? $__________ Answer = 4252.59 [Carrying amount of loan after 8th payment / PVIFA (2%, 4); Where carrying amount of loan after 8th payment = installment amount computed earlier * PVIFA (2.5%, 4) 5) Merlin has found that it will need $3,000,000 three years from today's date. What equal semi-annual payments starting today will Merlin have to pay into an account earning 6% per year [with semi-annual compounding] in order to accomplish this goal? The last payment into the account will be made three years from today. How large will each of these payments need to be for Merlin to accomplish this goal? $_________ Answer = $39,152