Answer:
a. $10,783.68
b. $10,510.36 semi annual compounding
Explanation:
a. This question requires the present value of $26,700 given 8 years and compounded annually at 12%.
Present Value = [tex]\frac{Future Value}{ ( 1 + interest)^{number of periods} }[/tex]
Present Value = [tex]\frac{26,700}{ 1.12^{8} }[/tex]
Present Value = $10,783.68
He would need to invest $10,783.68 today.
b. This is a duplicate of question 1 but I will solve it assuming semi-annual compounding just in case.
12% per annum would become = 12/2 = 6% per semi annum
Number of periods would become = 8 * 2 = 16 periods
Present Value = [tex]\frac{Future Value}{ ( 1 + interest)^{number of periods} }[/tex]
Present Value = [tex]\frac{26,700}{ 1.06^{16} }[/tex]
Present Value = $10,510.36
He would need to invest $10,510.36 today.
