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

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1/16/18
Lecture 1: Time Value of Money
Time Value of Money
āBasics
āPV: present value, the initial deposit, present value of an investment of money
āi: interest rate
ān: number of time periods
āFV: future, value at some specified future period
ām: number of compounding intervals within one year
āPMT: value of periodic payments
āKey relationship: compound interest
āAnnual Formula: FV = PV(1 + i)n
āMonthly Formula: FV = PV(1 + i/m)n*m
āPMT Formula: FV = Ī£t=1n-1 PMT(1 + i)t +PMT
Exercises
āUnknown FV
āDeposit \$10k today
āEarn annual interest of 6%
āWhat is the value of deposit after 1 year?
ā => FV = 10,000 + (10,000 * 0.06) = 10,600
āMultiple periods
āSuppose you leave the \$10k for 2 years
ā=> FV = 10,000(10,000 * 0.06)*(10,000 * 0.06) = 11,236
āCompounding monthly
āSuppose 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
āUnknown: PV
āConsider an investment that pays \$10.6k after 1 year
āIf investor requires a 6% return what price should be paid for the investment
today?
ā FV = PV(1 + i)n
āPV = FV / (1 + i)n
ā=> PV = 10,600 / (1 + 0.06)1 = 10,000
Annuities
āSo far we only have been doing a single deposit or payment made once
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āBut: many investments involve a series of equal deposits (or payments) made at equal
intervals over time
āE.g. mortgage payments
Exercises using PMT
āUnknown FV
ā Deposit \$1k at the end of each year for 5 years
āInterest compounded at annual rate of 5%
āHow much accumulated at the end of the period
ā FV of Payment 1
āDeposit \$1k at the end of Year 1
āEarns interest over 4 years
āFV1 = 1000 (1 + 0.05)4 = 1215.51
ā FV of Payment 2
āDeposit \$1k at the end of Year 2
āEarns interest over 3 years
āFV2 = 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
āPV of an Annuity
āAn investment provides annual cash receipts of \$500 for 6 years
āInvestor desires a 6% return
āHow 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
āSuppose we know what an investment will cost today and what the future stream of cash
flow is
āMain question: what is the implied yield or the return on the investment?
āIRR: internal rate of return
Exercise
āUnknown i: investments with single receipt
āCan buy one-acre lot today for \$5,639
āLot is expected to be worth \$15k after 7 years
āWhat 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%