# UGBA 180 Study Guide - Comprehensive Final Exam Guide - Mortgage Loan, Internal Rate Of Return, Interest Rate

UGBA 180

1/16/18

Lecture 1: Time Value of Money

Time Value of Money

āBasics

āPV: present value, the initial deposit, present value of an investment of money

āi: interest rate

ān: number of time periods

āFV: future, value at some specified future period

ām: number of compounding intervals within one year

āPMT: value of periodic payments

āKey relationship: compound interest

āAnnual Formula: FV = PV(1 + i)n

āMonthly Formula: FV = PV(1 + i/m)n*m

āPMT Formula: FV = Ī£t=1n-1 PMT(1 + i)t +PMT

Exercises

āUnknown FV

āDeposit $10k today

āEarn annual interest of 6%

āWhat is the value of deposit after 1 year?

ā => FV = 10,000 + (10,000 * 0.06) = 10,600

āMultiple periods

āSuppose you leave the $10k for 2 years

ā=> FV = 10,000(10,000 * 0.06)*(10,000 * 0.06) = 11,236

āCompounding monthly

āSuppose 6% rate is compounded monthly not annually

ā=> FV = PV(1 + i/m)n*m

ā=> FV = 10,000 (1 + 0.06/12)1*12= 10,616.78

āUnknown: PV

āConsider an investment that pays $10.6k after 1 year

āIf investor requires a 6% return what price should be paid for the investment

today?

ā FV = PV(1 + i)n

āPV = FV / (1 + i)n

ā=> PV = 10,600 / (1 + 0.06)1 = 10,000

Annuities

āSo far we only have been doing a single deposit or payment made once

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āBut: many investments involve a series of equal deposits (or payments) made at equal

intervals over time

āE.g. mortgage payments

Exercises using PMT

āUnknown FV

ā Deposit $1k at the end of each year for 5 years

āInterest compounded at annual rate of 5%

āHow much accumulated at the end of the period

ā FV of Payment 1

āDeposit $1k at the end of Year 1

āEarns interest over 4 years

āFV1 = 1000 (1 + 0.05)4 = 1215.51

ā FV of Payment 2

āDeposit $1k at the end of Year 2

āEarns interest over 3 years

āFV2 = 1000 (1 + 0.05)3 = 1157.63

ā And do it for next 5 years to get

ā FV = FV1 + FV2 + FV3 + FV4 + FV5

ā => = 5525.63

āPV of an Annuity

āAn investment provides annual cash receipts of $500 for 6 years

āInvestor desires a 6% return

āHow much should the investor pay for this investment today?

ā PV = FV / (1 + i)n for a single payment

ā For annuity: sum up the PV of each individual payment

ā PV = PMT / (1 + i)1 + PMT / (1 + i)2 + ā¦ + PMT / (1 + i)n

ā PV = 500 / (1 + 0.06)1 + 500/ (1 + 0.06)2 + .. + 500 / (1 + 0.06)6

ā => $2458.66

Determining Yields or IRR

āSuppose we know what an investment will cost today and what the future stream of cash

flow is

āMain question: what is the implied yield or the return on the investment?

āIRR: internal rate of return

Exercise

āUnknown i: investments with single receipt

āCan buy one-acre lot today for $5,639

āLot is expected to be worth $15k after 7 years

āWhat investment yield would be earned if we buy the lot today and resell it for

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## Document Summary

Pv: present value, the initial deposit, present value of an investment of money. Fv: future, value at some specified future period. M: number of compounding intervals within one year. Annual formula: fv = pv(1 + i)n. Monthly formula: fv = pv(1 + i/m)n*m. Pmt formula: fv = t=1 n-1 pmt(1 + i)t +pmt. Suppose you leave the k for 2 years. => fv = 10,000(10,000 * 0. 06)*(10,000 * 0. 06) = 11,236. Suppose 6% rate is compounded monthly not annually. => fv = 10,000 (1 + 0. 06/12)1*12= 10,616. 78. Consider an investment that pays . 6k after 1 year. Pv = fv / (1 + i)n. So far we only have been doing a single deposit or payment made once. But: many investments involve a series of equal deposits (or payments) made at equal intervals over time. Deposit k at the end of each year for 5 years. Interest compounded at annual rate of 5%