12 GM Chapter 7 Quiz

What is the value generated by the recurrence relation after 3 applications of the rule:

A₀ = 16 ; A_n+1 = 1.5 A_n (SF)

Camryn invests $7600 with a bank. He will be paid interest at the rate of 6% per annum, compounding monthly. What is the rate (r) that would be used in the recurrence relation model? (SF)

An investment of $6000 earns compounding interest at the rate of 4.2% per annum. A recurrence relation that can be used to model the value of the investment after n years is shown below.

A₀=6000 ; A_n+1=1.042 An

Determine how many years it takes for the value of the investment to first exceed $8000. (SF)

An investment of $5000 earns interest at 4.2%p.a., compounding monthly. The recurrence relation to model this investment is .... (SF)

• A₀ = 5000 ; A_n+1 = 1.042 A_n

• A₀ = 5000 ; A_n+1 = 1.0035 A_n

• A₀ = 5000 ; A_n+1 = 0.0035 A_n

• A₀ = 5000 ; A_n+1 = 0.042 A_n

A bank offers a loan at 7.5%p.a. compounding fortnightly. What is the effective annual interest rate of the loan? Round to 2 dec.pl (SF)

Ella is an expert investor and her bank has offered a great rate of 9.2%p.a., compounding quarterly. She does however, have the option of changing it to compound weekly. Should she choose to do this, and why? (SF)

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Tara won $3,000 from a singing contest. If she puts this money in an account that earns 7.9% interest compounded weekly, how much money will be in the account after 5 years? (SF)

Twelve years ago, Paige put $2500 in an account that pays an interest rate of 5.9% compounded semi-annually. She now plans to take the money in that account and invest it for a further 3 years in another account where interest is compounded monthly. If she would like to have $7000 at the end of the 3 years, what interest rate is required in the new account ? (CF)

• 11.11%

• 0.93%

• 9.3%

• 10.09%

Lateisha borrowed some money to pay for a new car. The annual percentage rate of interest for her loan was 5.85%, compounding monthly. She repaid the principal and all interest charged, a total sum of $4911.67, after 18 months. Determine how much Lateisha originally borrowed.(SF)

Josh is 17 yrs old and purchases some antiques that he estimates will appreciate (compound) at a rate of 6%p.a and be worth $45000 by the time he is 50. If the antiques actually grow in value at a average rate of 7.5%p.a over this time, how much extra will they be worth compared to his estimate? (CF)