Question

a) You have RM 33 750 in a brokerage account, and you plan to have an account totals

RM 72 863.72. You expect to earn 8% annually on the account. How many years will it take to reach your goal? (3 Marks)

b) If you deposit RM 27 590 in a bank account that pays 13% interest annually, how much will be in your account after 7 years? (2 Marks) c) How long does it take to double your money, given the interest rate is 10%? (2 Marks)

d) Find the amount to which RM 4000 will grow if it is 11% compounded quarterly for 7 years. (3 Marks)

e) It is now January 1 st 2015, and you will need RM 55 570 on January 1 st 2019, in 4 years. Your bank compounds interest at an 7% annual rate.

i) How much must you deposit today to have balance of RM 55 500 on January 1 st

2019? (2 Marks)

ii) How much do you have to deposit today if the bank uses semi-annually compounding? (3 Marks)

Answer 1

Answer (a):

PV = RM 33750

FV = RM 72863.72

r = 8% annually

$FV=PV(1+r)^n$

$72863.72=33750(1+0.08)^n$

$(1.08)^n=\frac{72863.72}{33750}$

$(1.08)^n=2.1589$

Take log of both side

$nln(1.08)=ln(2.1589)$

$n=\frac{ln(2.1589)}{ln(1.08)}=10$

This means at least 10 years will be needed to reach goal.

Answer (b):

PV = RM 27590

r = 13% interest annually

Time period = 7 years

$FV=PV(1+r)^n$

$FV=27590\times(1+0.13)^7$

$FV=64,908.39$

This means the account will have $64,908.39 after 7 years.

Answer (c):

PV = RM 27590

FV = RM 55180

r = 10% annually

$FV=PV(1+r)^n$

$55180=27590(1+0.10)^n$

$(1.10)^n=\frac{55180}{27590}$

$(1.10)^n=2$

Take log of both side

$nln(1.10)=ln(2)$

$n=\frac{ln(2)}{ln(1.10)}=7.27\approx7$

This means 7 years will be needed to double money.

Answer (d):

PV = RM 4000

r = 11% compounded quarterly

n = 7 years

$FV=PV\times (1+\frac{r}{m})^{mn}$

$FV=4000\times (1+\frac{0.11}{4})^{4\times7}$

$FV=4000\times (1+0.0275)^{28}$

$FV=\$8549.71$

Answer (e):

i):

FV = RM 55570

n = 4 years

r =7% annually

$PV=\frac{FV}{(1+r)^n}$

$PV=\frac{55570}{(1+0.07)^4}$

$PV=\$42394.09$

ii):

FV = RM 55570

n = 4 years

r =7% annually

$PV=\frac{FV}{(1+\frac{r}{m})^{mn}}$

$PV=\frac{55570}{(1+\frac{0.07}{2})^{2\times4}}$

$PV=\frac{55570}{(1+0.035)^{8}}$

$PV=\$42200.50$