Question

a. What is the relationship between discounting and​ compounding?

b. What is the relationship between the​ present-value factor and the annuity​ present-value factor?

c. What will 4,400 invested for 13 years at 12 percent compounded annually grow to?

ii. How many years it will take 570 to grow to 2727.22 if it is invested at 11 percent compounded annually?

iii. At what rate would 1500 have to be invested to grow to 6339.35 in 11years?

Answer 1

a) Discounting and Compounding both are used to adjust time value of money. The value of $1 today is more than the value of $1 1 year later. Compounding is used to calculate future value of present cash flow or money. Discounting is used to calculate present value of future cash flow or money.

Future Value = Present value * ( 1 + interest rate )

b) Present value factor is the discount factor of a future 1 period cash flow whereas present value of annuity factor is the discount factor of future cash flows of annuity payments.

c) PV = 4400 n = 13 rate = 12%

FV = 4400 * (1.12)¹³

FV = 19,200

c) ii PV = 570 FV = 2727.22 rate = 11%no of years = 15

c iii) PV = 1500 FV = 6339.35 n = 11

Rate of interest = ( 6339.35 / 1500 )^{(1 / 11)} - 1

Rate of interest = 14%