Chapter 15B and 15C - Annuities formula

Transcription

1 Chapter 15B and 15C - Annuities formula Finding the amount owing at any time during the term of the loan. A = PR n Q Rn 1 or TVM function on the Graphics Calculator Finding the repayment amount, Q Q = PRn R 1 R n 1 or TVM function on the Graphics Calculator Finding the number of repayments, n A = PR n Q Rn 1 and Trial and Error. or TVM function on the Graphics Calculator

2 Exercise 15B p Reducing balance loans (Find repayment value, Q) 13e Megan s loan of $ is charged interest at 7% p.a., interest adjusted monthly. Find the monthly repayment if the loan is fully repaid in: e) 20 years 15c John borrows $ and contracts to repay the loan over 10 years. Find the repayment value if the loan is repaid quarterly at: c) 10% p.a., interest charged quarterly Exercise 15C p Reducing balance loans (Find number of repayments, n) 4a Jim has a reducing balance loan of $3500 that he is using for a holiday and has agreed to repay it by monthly instalments of $ at a rate of 7.6% p.a. (interest debited monthly). Find the number of repayments needed to repay in full and this time in years. 6a Ben has contracted to repay a reducing balance loan of $9200 by fortnightly instalments of $ Interest is charged at 8.2% p.a. and adjusted fortnightly. Find how long it will take Ben to repay the loan in full. 9 Some time ago, Elizabeth took out a loan of $ Interest has been charged at 10.5% p.a. (adjusted monthly) and monthly repayments of $ have serviced the loan. If the amount still owing is $ : a how long ago was the loan taken out? b what was the term of the loan? 18 Grace has borrowed $ to set up a travel agency and is repaying the reducing balance loan by monthly instalments of $ at 5.85% p.a. (adjusted monthly). At present she still owes $ a How much longer will it take to reduce the amount Grace owes to $ ? b When will she have repaid the loan in full? c What was the term of the loan?

3 Annuities formula using a standard calculator (finding repayment amount, Q) Q = PRn R 1 R n 1 Rob wants to borrow $2800 for a new hi-fi system from a building society at 7.5% p.a., interest adjusted monthly. What would be Rob s monthly repayment if the loan is fully repaid in 1.5 years? P = 2800, Q =?, n = = 18 R = (1 + r 7.5/12 ) = (1 + ) = Q = PRn R 1 R n 1 = 2800 x = Using a standard calculator option: 2800 x ^18 x ( ) / ( ^18-1)

4 Annuities formula using Casio fx-9860g AU Graphics Calculator (finding repayment amount, Q) Rob wants to borrow $2800 for a new hi-fi system from a building society at 7.5% p.a., interest adjusted monthly. What would be Rob s monthly repayment if the loan is fully repaid in 1.5 years? [$164.95] Calculator values: Variable Use n The Number of repayments I% Annual (yearly) interest rate (% pa) PV Principal [original amount borrowed], but entered as NEGATIVE number PMT The repayment amount (regular repayments) FV The amount owing on the loan after the n repayments P/Y The number of repayments each year C/Y Number of times interest is debited each year Set calculator to Compound Interest mode Enter the values: n: Enter 1.5x12 PMT: Enter 0 (unknown) Press F4 to calculate the Payment

5 1 - Annuities formula using Casio fx-9860g AU Graphics Calculator (finding number of repayments) A reducing balance loan of $ is to be repaid with monthly instalments of $ at an interest rate of 7.5% p.a. (debited monthly). Find the number of monthly repayments. Set calculator to Compound Interest mode Enter the values: n: Enter 0 (unknown) PV: Enter PMT: Enter Press F1 to calculate the number of repayments n is 240 months It is 240/12 years = 20 years

6 1 - Annuities formula using a standard calculator (finding number of repayments) A = PR n Q Rn 1 R 1 A reducing balance loan of $ is to be repaid with monthly instalments of $ at an interest rate of 7.5% p.a. (debited monthly). Find the number of monthly repayments. P = 60000, Q = , n =?, R = (1 + r 7.5/12 ) = (1 + ) = Take a guess, say 200: A 200 = PR n Q Rn 1 = x = Not less than 0, take another guess, say 220: A 220 = PR n Q Rn 1 = Using a standard calculator option: x ( ^200) ( x ( ^200-1)) / ( ) 3. Not less than 0, take another guess, say 240: A 240 = PR n Q Rn 1 = n is 240 months It is 240/12 years = 20 years

7 2 - Annuities formula using Casio fx-9860g AU Graphics Calculator (finding number of repayments) Some time ago Petra borrowed $ to buy a car. Interest on this reducing balance loan has been charged at 9.2% p.a. (adjusted monthly) and she has been paying $ each month to service the loan. Currently she still owes $ How long ago did Petra borrow the money? Set calculator to Compound Interest mode Enter the values: n: Enter 0 (unknown) PV: Enter PMT: Enter FV: Enter Press F1 to calculate the number of repayments n is 12 months Borrow the money 1 year ago.

8 2 - Annuities formula using a standard calculator (finding number of repayments) A = PR n Q Rn 1 R 1 Some time ago Petra borrowed $ to buy a car. Interest on this reducing balance loan has been charged at 9.2% p.a. (adjusted monthly) and she has been paying $ each month to service the loan. Currently she still owes $ How long ago did Petra borrow the money? Do trail and error to get just over or equal P = 14000, Q = , n =?, R = (1 + r 9.2/12 ) = (1 + ) = Take a guess, say 20: A 20 = PR n Q Rn 1 = x = Not close to , take another guess, say 11: A 11 = PR n Q Rn 1 = Close, take another guess, say 12: A 12 = PR n Q Rn 1 = n is 12 months, so she borrowed the money 1 year ago. Using a standard calculator option: x ( ^20) ( x ( ^20-1)) / ( )

9 End of Lesson