Quiz about Reducing-Balance Loans Review

Question 1

A reducing-balance loan is modelled by the recurrence relation $$A_0=25000,\ A_{n+1}=1.007 imes A_n-400$$ where $$A_n$$ is the balance of the loan after $$n$$ months. The balance of the loan after 5 months is:

Accepted Answer

$23 859.14

Answer

$23 626.15

Answer

$24 090.51

Answer

$25 887.34

Question 2

Hermione borrows $18 000 and will be charged compound interest at the rate 6.96% per annum compounding monthly. Hermione will repay the loan with monthly repayments of $850. If $$A_n$$ is the balance of the loan after $$n$$ months, a recurrence relation model for this reducing balance loan is:

Accepted Answer

$$A_0=18000,\ A_{n+1}=1.0058 imes A_n-850$$

Answer

$$A_0=18000,\ A_{n+1}=1.0174 imes A_n-850$$

Answer

$$A_0=18000,\ A_{n+1}=1.0696 imes A_n-850$$

Answer

$$A_0=18000,\ A_{n+1}=1.0174 imes A_n-1242$$

Question 3

What is the principal of this loan?

Accepted Answer

$15 000

Answer

$97.50

Answer

$500.00

Answer

$12 961.16

Question 4

What is the value of A, the reduction in principal by repayment number 3?

Accepted Answer

$407.75

Answer

$312.87

Answer

$497.37

Answer

$500.00

Question 5

The interest charged on this loan compounds monthly and monthly repayments are made. The annual percentage rate of interest for this loan is closet to:

Accepted Answer

7.8%

Answer

6.5%

Answer

6.67%

Answer

8.01%

Question 6

A reducing-balance loan has principal $180 000 and will be repaid with monthly repayments of $1500. The interest rate for this loan is 6.5% per annum, compounding monthly.

Using the annuities formula, the balance of this loan after two years will be:

Accepted Answer

$166 583.04

Answer

$144 000

Answer

$167 667.37

Answer

$173 508.88

Question 7

Mei Hui has borrowed $28 000 and will be charged compound interest at the rate of 6.4% per annum compounding monthly. She will repay this loan with exactly 24 repayments. The monthly repayment amount is closest to:

Accepted Answer

$1246

Answer

$850

Answer

$1046

Answer

$2415

Question 8

A reducing-balance loan with principal $40 000 is repaid with monthly repayments of $550. The annual interest rate is 5.2%. How many repayments does it take to reduce the balance of this loan below $35 000?

Accepted Answer

13

Answer

10

Answer

11

Answer

12

Question 9

If the balance of a reducing-balance loan with principal $175 000 has been reduced to $89 573.97 after 35 quarterly repayments of $4218, the annual percentage rate of interest for the loan is closest to:

Accepted Answer

5.2%

Answer

5.4%

Answer

5.6%

Answer

5.8%

Question 10

A loan of $6000, plus interest, is to be repaid with exactly 12 quarterly repayments. Interest charged at the rate of 10% per annum, compounding quarterly. If the first 11 repayments are of value $580, the 12th and final repayment must be:

Accepted Answer

$647.91

Answer

$228.97

Answer

$351.03

Answer

$580.00

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