question archive A loan will be repaid by month-end repayments of 3,000 for 10 years
A loan will be repaid by month-end repayments of 3,000 for 10 years
Subject:FinancePrice:2.86 Bought22
A loan will be repaid by month-end repayments of 3,000 for 10 years. The interest rate is 1.3% p.a. compounded monthly for the first 6 years and 9.1% p.a. compounded monthly thereafter. How much is the loan? Correct your answer to the nearest cent without any units.
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| PVOrdinary Annuity = C*[(1-(1+i/(f*100))^(-n*f))/(i/(f*100))] |
| C = Cash flow per period |
| i = interest rate |
| n = number of payments I f = frequency of payment |
| PV= 3000*((1-(1+ 9.1/1200)^(-4*12))/(9.1/1200)) |
| PV = 120324.62 |
| Using Calculator: press buttons "2ND"+"FV" then assign |
| PMT =3000 |
| I/Y =9.1/12 |
| N =4*12 |
| FV = 0 |
| CPT PV |
| Using Excel |
| =PV(rate,nper,pmt,FV,type) |
| =PV(9.1/(12*100),12*4,,PV,) |
| PVOrdinary Annuity = C*[(1-(1+i/(f*100))^(-n*f))/(i/(f*100))] |
| C = Cash flow per period |
| i = interest rate |
| n = number of payments I f = frequency of payment |
| PV= 3000*((1-(1+ 1.3/1200)^(-6*12))/(1.3/1200)) |
| PV = 207682.67 |
| Using Calculator: press buttons "2ND"+"FV" then assign |
| PMT =3000 |
| I/Y =1.3/12 |
| N =6*12 |
| FV = 0 |
| CPT PV |
| Using Excel |
| =PV(rate,nper,pmt,FV,type) |
| =PV(1.3/(12*100),12*6,,PV,) |
| EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100 |
| ? = ((1+1.3/(12*100))^12-1)*100 |
| Effective Annual Rate% = 1.3078 |
| Future value = present value*(1+ rate)^time |
| 120324.62 = Present value*(1+0.013078)^6 |
| Present value = 111300.52 |
| Using Calculator: press buttons "2ND"+"FV" then assign |
| FV =-120324.62 |
| I/Y =1.3078 |
| N =6 |
| PMT = 0 |
| CPT PV |
| Using Excel |
| =PV(rate,nper,pmt,FV,type) |
| =PV(0.013078,6,,120324.62,) |
Total = 111300.52+207682.67
=318983.19
