I. Find the present and future value of $1000 received every month end for 20 years if the interest rate is J12 = 12% p.a. (5 marks)
II. Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years. (5 marks).
III. John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account? (10 Marks)
Answers
Find the present and future value of $1000 received every month end for 20 years if the interest rate is J12 = 12% p.a. (5 marks)
II. Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years. (5 marks).
Step-by-step explanation:
I) im=1.12^{\frac{1}{12}}=1.0095im=1.12 ¹² /¹
=1.0095
im- rate in month
FV=1000*\frac{1.0095^{240}-1}{1.0095-1}=912,845.15FV=1000∗
1.0095−1
1.0095 ²⁴⁰ −1 =912,845.15
FV-future value
PV=1000*\frac{(\frac{1}{1.0095})^{240}-1}{\frac{1}{1.0095}-1}=95,282.58PV=1000∗
1.0095
1
−1
(
1.0095
1
)
240
−1
=95,282.58
PV-present value
II) PV=10,000*\frac{(\frac{1}{1.12})^{30}-1}{\frac{1}{1.12}-1}-\frac{(\frac{1}{1.12})^{10}-1}{\frac{1}{1.12}-1}=26,971.52PV=10,000∗
1.12
1
−1
(
1.12
1
)
30
−1
−
1.12
1
−1
(
1.12
1
)
10
−1
=26,971.52
III) 55-70=15\ years55−70=15 years
2,000*\frac{1.06^{45}-1}{1.06-1}-\frac{1.06^{30}-1}{1.06-1}=267,370.652,000∗
1.06−1
1.06
45
−1
−
1.06−1
1.06
30
−1
=267,370.65
267,370.65-10,000*1.06^{30}=209,936.14267,370.65−10,000∗1.06
30
=209,936.14
209,936.14=x*\frac{1.06^{30}-1}{1.06-1}209,936.14=x∗
1.06−1
1.06
30
−1
x=2,655.47x=2,655.47