Answer to Question #119695 in Financial Math for Piya

Question

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)

Answer 1

I) $im=1.12^{\frac{1}{12}}=1.0095$

im- rate in month

$FV=1000*\frac{1.0095^{240}-1}{1.0095-1}=912,845.15$

FV-future value

$PV=1000*\frac{(\frac{1}{1.0095})^{240}-1}{\frac{1}{1.0095}-1}=95,282.58$

PV-present value

II) $PV=10,000*\frac{(\frac{1}{1.12})^{30}-1}{\frac{1}{1.12}-1}-\frac{(\frac{1}{1.12})^{10}-1}{\frac{1}{1.12}-1}=26,971.52$

III) $55-70=15\ years$

$2,000*\frac{1.06^{45}-1}{1.06-1}-\frac{1.06^{30}-1}{1.06-1}=267,370.65$

$267,370.65-10,000*1.06^{30}=209,936.14$

$209,936.14=x*\frac{1.06^{30}-1}{1.06-1}$

$x=2,655.47$