- 1、下载文档前请自行甄别文档内容的完整性,平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益,请联系客服反馈,我们会尽快为您处理(人工客服工作时间:9:00-18:30)。
◦ PV0 = FVn (PV= $30,000 * 0.823
= $246,900
Your firm has been told that it needs $74,300 today to fund a $120,000 expense 6 years from now. What rate of interest was used in the computation?
FVn=PV0 (FVIFi,n) (FVIFi,8) = FV8/PV0
= 3,000/1,000
=3
i= 14.68%
How long would it take for an investment of $1,000 to grow to $1,900 if we invested it at a compound annual interest rate of 10 percent?
SI = P0(i)(n)
SI: Simple Interest P0: Deposit today (t=0) i: Interest Rate per Period n:Number of Time Periods
Assume that you deposit $1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year?
What is the Present Value (PV) of the previous problem?
The Present Value is simply the $1,000 you originally deposited. That is the value today!
P0 = FV - SI Present Value is the current value of a future
Present Value
Value today of a future cash
flow.
Discount Rate
Interest rate used to compute
present values of future cash flows.
Discount Factor
Present value of a $1 future payment.
TIME allows you the opportunity to postpone consumption and earn INTEREST.
Simple Interest
Interest paid (earned) on only the original amount, or principal, borrowed (lent).
Which would you prefer -- $10,000 today or $10,000 in 5 years?
Obviously, $10,000 today.
The reason is that there is TIME VALUE OF MONEY!!
Why is TIME such an important element in your decision?
Period 1 2 3 4 5
6% 1.060 1.124 1.191 1.262 1.338
7% 1.070 1.145 1.225 1.311 1.403
8% 1.080 1.166 1.260 1.360 1.469
Julie Miller wants to know how large her deposit of $10,000 today will become at a compound annual interest rate of 10% for 5 years.
Time Value of Money
The Interest Rate Simple Interest Compound Interest Compounding More Than Once
per Year Amortizing a Loan
Future Value
Amount to which an investment will grow after earning interest
FV1 = P0(1+i)1 FV2 = P0(1+i)2
General Future Value Formula: FVn = P0 (1+i)n
or FVn = P0 (FVIFi,n) See Table I
FVIFi,n is on Table I at the end of the book
0 7%
1
2
$1,000
FV2
FV1 = P0 (1+i)1 = $1,000 (1.07) = $1,070
Compound Interest
You earned $70 interest on your $1,000 deposit over the first year.
This is the same amount of interest you would earn under simple interest.
Ordinary Annuity: Payments or receipts occur at the end of each period.
0 1 2 3 45
10%
$10,000
FV5
Calculation based on general formula: FVn = P0 (1+i)n FV5 = $10,000 (1+ 0.10)5 = $16,105.10
Calculation based on Table I:
FV5 = $10,000 (FVIF10%, 5) = $10,000 (1.611) = $16,110 [Due to Rounding]
Compound Interest
• Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent).
• Interest on Interest
Formula
=$1,000,000 * 10.835
= $10,835,000
You need $30,000 in cash to buy a house 4 years from today. You expect to earn 5 percent on your savings. How much do you need to deposit today if this is the only money you save for this purpose?
amount of money, or a series of payments, evaluated at a given interest rate.
Future Value of a Single $1,000 Deposit
Future Value (U.S. Dollars)
20000
15000
Quick! How long does it take to double $5,000 at a compound rate of 12% per
year (approx.)?
We will use the “Rule-of-72”
a) 72 / 12% = 6 Years or b) 72/ 6 years = 12%
SI
= P0(i)(n)
= $1,000(.07)(2)
= $140
What is the Future Value (FV) of the deposit?
FV = P0 + SI = $1,000 + $140 = $1,140
Future Value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate.
Assume that you need $1,000 in 2 years. Let’s examine the process to determine how much you need to deposit today at a discount rate of 7% compounded annually.
= $6,210.00 [Due to Rounding]
If you invest $1,000 today, you will receive $3,000 in exactly 8 years. What is the compound interest rate implicit in this situation?
PVIFi,n is on Table II at the end of the book
Period 6%
7%
8%
1
.943 .935 .926
2
.890 .873 .857
3
.840 .816 .794
4
.792 .763 .735
5
.747 .713 .681
Julie Miller wants to know how large of a deposit to make so that the money will grow to $10,000 in 5 years at a discount rate of 10%.