Question #281475

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)

Expert's answer

**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"

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