Chapter 03& 04 : Banking What is the Bank ? 1. Receive Deposits 2. Grant Loans 3. Other services

Bank and Economy Borrowers-Spenders Banks or MFIs Depositors - Lenders Pay Interest Pay Interest Pay Interest Banks or MFIs

There are two types of interest in the Economy Simple Interest karR)ak;eTal Interest karR)ak; Compound Interest karR)ak;smas

Simple Interest Simple Interest: The interest on a loan that charges interest only for the period of time. KWCakarR)ak;EdlKitEtelIR)ak;edIm¬Edl)anx©I¦kñúgRKb;ry³eBl. Formula of Interest: I= Prt where : I= Interest ($ ) P= Principal r= Interest rate ( %) per year t = period of time

Future Value of Simple Interest or Total Amount: FV = P +I = P + Prt = P( 1 + rt ) or FV = PV ( 1 + rt ) where PV = Present Value

2. Compound Interest : karR)ak;smas KWCakarR)ak;elIkarR)ak; . RtUv)aneKeRbIR)as;sMrab;hirBaØvtßúry³eBlEvg. ¬karR)ak; bUkCamYyR)ak;edImedIb,ITUTat;eTARKaeRkay ¦

Future Value and Present Value Future Value (FV) is what money today will be worth at some point in thefuture. tMélGnaKtCaluyenAéf¶enHnwgCaluynaeBlGnaKt. Present Value (PV) is what money at some point in the future is worth today. tMélbc©úb,nñCaluykñúgeBl GnaKtCaluyenAéf¶enH.

Figure 9-1 Relationship of present value and future value $ $1,464.10 future value $1,000 present value 10% interest 1 2 3 4 Number of periods

Formula of FV and PV

FV2 FV1 FV3 FVt-1 FVt PV t 3 t-1 2 1

Proof :

m :cMnYndgénkarTUTat; General Formula m :cMnYndgénkarTUTat;

Use The MS Excel: FV and PV FV( rate, nper, pmt,[pv],[type]) where: -rate: CaGRtakarR)ak;kñúgRKa Nper: cMnYnRKa Pmt: CacMnYnTwkR)ak;Edlbg;tamkalnImYy² PV: CatMélbc©úb,nñ Type: sMrab;kMNt;ry³eBlCak;EsþgEdleyIgRtUvbg;EdlmanCMerIsBI KW 0 nig 1 Edl 0 eRbIsMrab;krNIbg;cugRKa 1 eRbIsMrab;krNIbg;edImRKa

Single Amount of FV and PV You should type the formula: =fv( rate,nper,0, -pv, 0) =pv(rate, nper,0,-fv,0)

Example: PV = $1,000 t = 5 years r = 10% FV = ?

Annuities Annuity: a stream or series of equal payments to be received in the future The payments are assumed to be received at the end of each period (unless stated otherwise) A good example of an annuity is a lease, where a fixed monthly charge is paid over a number of years

Future Value of An Annuity ( FVA) An annuity is set up in which there are yearly payments of $200 for 5 years with interest being paid at the annual rate of 6% compounded annually. Find the amount of the annuity. 4 2 3 5 1 $200 $200 $200 $200 $200

Formula of FVA

Proof: t-1 2 3 t 1 $A $A $A $A $A FV0 FV1 FVt-1 20

Formula

In Ms Excel in computing FVA a) Ordinary of FVA =fv(rate,nper, -pv,0,0) b) FVA of Annuity Due: =fv(rate, nper,-pv,0,1)

Present Value of An Annuity ( PVA) General Formula of PVA

Present Value of An Annuity ( PVA) 2 3 t-1 1 $A $A $A $A $A PV1 PV2 PVt 25

Present Value of An Annuity ( PVA) An annuity is set up in which there are yearly payments of $200 for 5 years with interest being paid at the annual rate of 6% compounded annually. Find the amount of the annuity. 4 2 3 5 1 $200 $200 $200 $200 $200 28

Example: How much money you will deposit today in your account which pays 8% interest per year, you could withdrawal $100 at the end of each year for the next five years ?

Ms Excel of PVA Ordinary of PVA =pv(rate,nper,-pv,0,0) b)PVA of Annuity Due: =pv(rate, nper,-pv,0,1)

What is the power of your money ?

Poor can help but Lazy cannot help