Week 8 FIN111
Week 8- Time Value of Money
Critical Thinking
5.1
“A dollar today is worth more than a dollar tomorrow’ because todays dollar can be invested to earn interest or spent. Because of this fact, an entity requires compensation through interest, for deferring consumption (spending). The value of that dollar invested grows over time and the interest rate reflects the trade-off between spending today versus saving.
5.5
Compounding:
Is concerned with finding the future value of an investment.
Is the process of converting the initial amount (principal PV) into future value (FV)
Involves calculating interest earned on principal and on interest received
Equation for compounding (finding future value): FVn = PV x (1+i)^n
Where n = no. of periods, i = interest rate, FV= future value, PV = present value (principal)
Discounting:
Is concerned with finding the present value of an investment.
Is the process of calculating the current value (or present value) of a future cash flow.
The present value can be thought of as the discounted value of a future amount.
The interest rate i, is known as the discount rate.
Where compounding involves calculating an amount in the future, present value involves the reverse
Equation for discounting: PV = FVn / (1+i)^n
Where PV = present value, FV = future value, i = discounted rate, n= number of periods
Questions and Problems:
5.5
PV = $2700, i = 5% or 0.05, n = 4, m = 2
Equation for compounding more than once a year:
FVn = PV x (1+i/m)^m x n
FVn= $2700 x (1+0.05/2)^4x2
FVn=$2700 x (1+0.025)^8
FVn=$3289.69 (the amount you will expect in 4 years time after investment)
5.12
FVn = $70,000, i = 9.25% or 0.0925, n= 5
Equation for present value:
PV = FVn / (1+i)^n
PV = $70,000 / (1+0.0925)^5
PV= $44, 977.03
Thus the amount Tracy will need to invest today to get her 20% deposit in 5 years.
5.15
Bank loan:
PV= $1300, i = 6.5%, n = 2
FV= PV x (1+i)^n
FV = $1300 x (1 + 0.065)^2
FV = $1474.49
Therefore you should
Critical Thinking
5.1
“A dollar today is worth more than a dollar tomorrow’ because todays dollar can be invested to earn interest or spent. Because of this fact, an entity requires compensation through interest, for deferring consumption (spending). The value of that dollar invested grows over time and the interest rate reflects the trade-off between spending today versus saving.
5.5
Compounding:
Is concerned with finding the future value of an investment.
Is the process of converting the initial amount (principal PV) into future value (FV)
Involves calculating interest earned on principal and on interest received
Equation for compounding (finding future value): FVn = PV x (1+i)^n
Where n = no. of periods, i = interest rate, FV= future value, PV = present value (principal)
Discounting:
Is concerned with finding the present value of an investment.
Is the process of calculating the current value (or present value) of a future cash flow.
The present value can be thought of as the discounted value of a future amount.
The interest rate i, is known as the discount rate.
Where compounding involves calculating an amount in the future, present value involves the reverse
Equation for discounting: PV = FVn / (1+i)^n
Where PV = present value, FV = future value, i = discounted rate, n= number of periods
Questions and Problems:
5.5
PV = $2700, i = 5% or 0.05, n = 4, m = 2
Equation for compounding more than once a year:
FVn = PV x (1+i/m)^m x n
FVn= $2700 x (1+0.05/2)^4x2
FVn=$2700 x (1+0.025)^8
FVn=$3289.69 (the amount you will expect in 4 years time after investment)
5.12
FVn = $70,000, i = 9.25% or 0.0925, n= 5
Equation for present value:
PV = FVn / (1+i)^n
PV = $70,000 / (1+0.0925)^5
PV= $44, 977.03
Thus the amount Tracy will need to invest today to get her 20% deposit in 5 years.
5.15
Bank loan:
PV= $1300, i = 6.5%, n = 2
FV= PV x (1+i)^n
FV = $1300 x (1 + 0.065)^2
FV = $1474.49
Therefore you should