Further Maths Help

[PopcornTime]

Hey,

Would really appreciate it if someone could help me out with the below questions.

The amount of money in a bank account after n years, Vn, can be modelled by the following recurrence relation.

V0 = 12000, Vn+1 = 0.92Vn

The amount of money is:
a) growing at rate of 9.2% pa
b) growing at a rate of 8% pa
c) neither growing nor decaying
d) decaying at a rate of 9.2% per annum
e) decaying at a rate of 8% per annum

A musician purchased a new grand piano for $17990. After 8 years, it will have an estimated value of $12500. If the value of the paint is depreciated using a reduced-balanced method, the annual rate of depreciation is closest to:
a) 4.45%
b) 4.66%
c) 30.5%
d) 43.9%
e) 69%

An amount of money is deposited into an account with BankAus. BankAus will pay simple interest at a rate of 4.5% pa. Which of the following conditions, offered by BankNZ will earn more interest in one year than the account with BankAus?

a) 4.2% pa simple interest
b) 4.4% pa, compounding quarterly
c) 4.45% pa, compounding monthly
d) 4.3% pa, compounding fortnightly
e) 4.4% pa, compounding weekly

Thanks!

[devavasa14]

Hey,

Would really appreciate it if someone could help me out with the below questions.

The amount of money in a bank account after n years, Vn, can be modelled by the following recurrence relation.

V0 = 12000, Vn+1 = 0.92Vn

The amount of money is:
a) growing at rate of 9.2% pa
b) growing at a rate of 8% pa
c) neither growing nor decaying
d) decaying at a rate of 9.2% per annum
e) decaying at a rate of 8% per annum

A musician purchased a new grand piano for $17990. After 8 years, it will have an estimated value of $12500. If the value of the paint is depreciated using a reduced-balanced method, the annual rate of depreciation is closest to:
a) 4.45%
b) 4.66%
c) 30.5%
d) 43.9%
e) 69%

An amount of money is deposited into an account with BankAus. BankAus will pay simple interest at a rate of 4.5% pa. Which of the following conditions, offered by BankNZ will earn more interest in one year than the account with BankAus?

a) 4.2% pa simple interest
b) 4.4% pa, compounding quarterly
c) 4.45% pa, compounding monthly
d) 4.3% pa, compounding fortnightly
e) 4.4% pa, compounding weekly

Thanks!

Hello,

The first Q is compound interest:  Vo=principal, Vn+1=RxVn  R=1+(r/t)/100 
where r=interest rate, t=compounded amount

0.92=1+(r/1)/100 >>>>CAS
r=-8   Therefore, decaying at 8% pa, decaying because the rate is negative. E

The second Q is reducing balance depreciation:  Vn=(1-(r/100))^n x Vo      Where r=depreciation rate
I'm sorry that the brackets are hard to understand but it's saying 1 minus (r/100) all to the power of the number of years (n). Soooo...
12500=(1-(r/100))^8 x 17990 >>>>>CAS
r=4.45%  A

I'm sorry but I don't know how to do the last question.
I hope you understand it better now though