## Future value and present value problems

Solutions to Present Value Problems Present Value: Solutions Problem 1 a. Current Savings Needed = \$ 500,000/1.110 = \$ 192,772 b. Annuity Needed = \$ 500,000 (APV,10%,10 years) = \$ 31,373 Problem 2 Present Value of \$ 1,500 growing at 5% a year for next 15 years = \$ 18,093 Future Value = \$ 18093 (1.08^15) = \$ 57,394 Problem 3

Example: Sam promises you \$500 next year, what is the Present Value? To take a future payment backwards one year divide by 1.10 So \$500 next year is \$500 ÷ 1.10 = \$454.55 now (to nearest cent). Chapter 2 Present Value 2-7 3 Real vs. Nominal CFs and Rates Nominal vs. Real CFs Inﬂation is 4% per year. You expect to receive \$1.04 in one year, what is this CF really worth next year? The real or inﬂation adjusted value of \$1.04 in a year is Real CF = Nominal CF 1+inﬂation = 1.04 1+0.04 =\$1.00. In general, at annual inﬂation rate of i we have (Real CF)t = The value of a typical corporate bond is the present value of an annuity plus the present value of a lump sum. Thus, if an individual does not understand how to calculate the present value of a lump sum or the present value of an annuity, it is difficult to determine the value of a typical corporate bond. Any value that occurs at the beginning of the problem (or the beginning of a part of the problem) is a present value. The key is that the present value occurs before any other cash flows. Usually, when a present value is given, it will be surrounded by words indicating that an investment happens today. Present value is the value right now of some amount of money in the future. For example, if you are promised \$110 in one year, the present value is the current value of that \$110 today. Present value is one of the foundational concepts in finance, and we explore the concept and calculation of present value in this video.

## There are two ways of calculating future value: simple annual interest and annual compound interest. Future value with simple interest is calculated in the following manner: Future Value = Present Value x [1 + (Interest Rate x Number of Years)] For example, Bob invests \$1,000 for five years with an interest rate of 10%. The future value would be \$1,500.

Calculate the present value of a future value lump sum of money using pv = fv / (1 + i)^n. The present value investment for a future value return. Demonstrate the use of timelines in time value of money problems. 1 These notes were future”. The process of calculating the present value of a future cash. 13 Apr 2018 When solving for the present value of future cash flows, the problem is one of discounting, rather than growing, and the required expected  Present value calculator, formula, real world and practice problems to values, future value, interesting rate and time periods, and calculate the present value of   1 Apr 2016 So how do we tackle the question of value over time? Future Value. Let's take our \$1,000 today and see what that might be worth in a year's time  Return value. future value. Syntax. =FV (rate, nper, pmt, [pv], [type]). Arguments. rate - The interest rate per period. nper - The total number of payment periods.

### Find the future value of Rs. 100,000 for 15 years. The current five-year rate is 6%. Rates for the second and third five-year periods and expected to be 6.5% and 7.5%, respectively.

future value = \$5,000 interest rate = 5% number of periods = 6 We want to solve for the present value. present value = future value / (1 + interest rate) number of periods. or, using notation. PV = FV/ (1 + r) t. Inserting the known information, PV = \$5,000 / (1 + 0.05) 6. PV = \$5,000 / (1.3401) PV = \$3,731 The future value (F) equals the present value (P) times e (Euler's Number) raised to the (rate * time) exponential. For example: Bob again invests \$1000 today at an interest rate of 5%. After 10 years, his investment will be worth: \$\$ F=1000*e^{.05*10} = 1,648.72 \$\$ Future value with simple interest is calculated in the following manner: Future Value = Present Value x [1 + (Interest Rate x Number of Years)] For example, Bob invests \$1,000 for five years with an interest rate of 10%. The future value would be \$1,500. Future Value = \$1,000 x [1 + Present value is the sum of money that must be invested in order to achieve a specific future goal. Future value is the dollar amount that will accrue over time when that sum is invested. The 5. Complete the following, solving for the present value, PV: Case Future value Interest rate Number of periods Present value A \$10,000 5% 5 \$7,835.26 B \$563,000 4% 20 \$256,945.85 C \$5,000 5.5% 3 \$4,258.07 6. Suppose you want to have \$0.5 million saved by the time you reach age 30 and suppose that you are 20 years old today.

### Explain the concepts of future value, present value, annuities, and discount rates Perform complex time value of money calculations (problems where multiple

Find the future value of Rs. 100,000 for 15 years. The current five-year rate is 6%. Rates for the second and third five-year periods and expected to be 6.5% and 7.5%, respectively. The future value of an annuity is the total value of payments at a specific point in time. The present value is how much money would be required now to produce those future payments. future value = \$5,000 interest rate = 5% number of periods = 6 We want to solve for the present value. present value = future value / (1 + interest rate) number of periods. or, using notation. PV = FV/ (1 + r) t. Inserting the known information, PV = \$5,000 / (1 + 0.05) 6. PV = \$5,000 / (1.3401) PV = \$3,731 The future value (F) equals the present value (P) times e (Euler's Number) raised to the (rate * time) exponential. For example: Bob again invests \$1000 today at an interest rate of 5%. After 10 years, his investment will be worth: \$\$ F=1000*e^{.05*10} = 1,648.72 \$\$

## 5. Complete the following, solving for the present value, PV: Case Future value Interest rate Number of periods Present value A \$10,000 5% 5 \$7,835.26 B \$563,000 4% 20 \$256,945.85 C \$5,000 5.5% 3 \$4,258.07 6. Suppose you want to have \$0.5 million saved by the time you reach age 30 and suppose that you are 20 years old today.

The future value of an annuity is the total value of payments at a specific point in time. The present value is how much money would be required now to produce those future payments. future value = \$5,000 interest rate = 5% number of periods = 6 We want to solve for the present value. present value = future value / (1 + interest rate) number of periods. or, using notation. PV = FV/ (1 + r) t. Inserting the known information, PV = \$5,000 / (1 + 0.05) 6. PV = \$5,000 / (1.3401) PV = \$3,731 The future value (F) equals the present value (P) times e (Euler's Number) raised to the (rate * time) exponential. For example: Bob again invests \$1000 today at an interest rate of 5%. After 10 years, his investment will be worth: \$\$ F=1000*e^{.05*10} = 1,648.72 \$\$ Future value with simple interest is calculated in the following manner: Future Value = Present Value x [1 + (Interest Rate x Number of Years)] For example, Bob invests \$1,000 for five years with an interest rate of 10%. The future value would be \$1,500. Future Value = \$1,000 x [1 + Present value is the sum of money that must be invested in order to achieve a specific future goal. Future value is the dollar amount that will accrue over time when that sum is invested. The

Explain the concepts of future value, present value, annuities, and discount rates Perform complex time value of money calculations (problems where multiple  Online Future Value Calculator. Compute future returns on investments with Wolfram|Alpha. Assuming present and future value  To experiment with a future value table, determine how much \$1 would grow to in 10 periods at 5% per period. The answer to this question is \$1.63 and can be  Present value (PV) and future value (FV) are measures of worth based on the concept of time value of money and discounted cash flow. PV represents the  Calculate the present value of a future value lump sum of money using pv = fv / (1 + i)^n. The present value investment for a future value return.