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

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Lecture 1: Time Value of Money
Time Value of Money
Basics
PV: present value, the initial deposit, present value of an investment of money
i: interest rate
n: number of time periods
FV: future, value at some specified future period
m: number of compounding intervals within one year
PMT: value of periodic payments
Key relationship: compound interest
Annual Formula: FV = PV(1 + i)n
Monthly Formula: FV = PV(1 + i/m)n*m
PMT Formula: FV = Σt=1n-1 PMT(1 + i)t +PMT
Exercises
Unknown FV
Deposit \$10k today
Earn annual interest of 6%
What is the value of deposit after 1 year?
=> FV = 10,000 + (10,000 * 0.06) = 10,600
Multiple periods
Suppose you leave the \$10k for 2 years
=> FV = 10,000(10,000 * 0.06)*(10,000 * 0.06) = 11,236
Compounding monthly
Suppose 6% rate is compounded monthly not annually
=> FV = PV(1 + i/m)n*m
=> FV = 10,000 (1 + 0.06/12)1*12= 10,616.78
Unknown: PV
Consider an investment that pays \$10.6k after 1 year
If investor requires a 6% return what price should be paid for the investment
today?
FV = PV(1 + i)n
PV = FV / (1 + i)n
=> PV = 10,600 / (1 + 0.06)1 = 10,000
Annuities
So far we only have been doing a single deposit or payment made once
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Unlock all 89 pages and 3 million more documents. But: many investments involve a series of equal deposits (or payments) made at equal
intervals over time
E.g. mortgage payments
Exercises using PMT
Unknown FV
Deposit \$1k at the end of each year for 5 years
Interest compounded at annual rate of 5%
How much accumulated at the end of the period
FV of Payment 1
Deposit \$1k at the end of Year 1
Earns interest over 4 years
FV1 = 1000 (1 + 0.05)4 = 1215.51
FV of Payment 2
Deposit \$1k at the end of Year 2
Earns interest over 3 years
FV2 = 1000 (1 + 0.05)3 = 1157.63
And do it for next 5 years to get
FV = FV1 + FV2 + FV3 + FV4 + FV5
=> = 5525.63
PV of an Annuity
An investment provides annual cash receipts of \$500 for 6 years
Investor desires a 6% return
How much should the investor pay for this investment today?
PV = FV / (1 + i)n for a single payment
For annuity: sum up the PV of each individual payment
PV = PMT / (1 + i)1 + PMT / (1 + i)2 + … + PMT / (1 + i)n
PV = 500 / (1 + 0.06)1 + 500/ (1 + 0.06)2 + .. + 500 / (1 + 0.06)6
=> \$2458.66
Determining Yields or IRR
Suppose we know what an investment will cost today and what the future stream of cash
flow is
Main question: what is the implied yield or the return on the investment?
IRR: internal rate of return
Exercise
Unknown i: investments with single receipt
Can buy one-acre lot today for \$5,639
Lot is expected to be worth \$15k after 7 years
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%

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