Question - Present and Future Values

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?