In: Finance
Question 10
What is the future value of a five-year ordinary annuity of $1,000 per year if the interest rate is 4.30%? Hint: solve for year 5.
Question 11
What is the present value of a perpetuity that offers to pay $100 next year and every year after the payment grows at 4.9%. Investments with similar risk are offering an 8% annual return.
Question 10:
P = Annual payment = $1,000
n = 5 years
r = interest rate = 4.30%
Future Value = P * [(1+r)^n - 1] / r
= $1,000 *[(1+4.30%)^5 - 1] / 4.30%
= $1,000 * 0.23430231101 / 0.043
= $5,448.89095380099
= $5,448.89
Therefore, Future value of annuity is $5,448.89
Question 11:
P = First payment = $100
r = annual return = 8%
g = growth rate = 4.9%
Present Value of perpetuity = P / (r-g)
= $100 / (8% - 4.9%)
= $100 / 0.031
= $3,225.80645
Therefore, present value of perpetuity is $3,225.81