Compound Interest Loans and Investments

$450 is invested in an account paying a compound interest rate of 3.75%  p.a. The recurrence relation for the value of the investment after 𝑛 years is

• A_n+1=1.0375 A₀=450

• A_n+1=450+A_n, A₀=450

• A_n+1=450+d A₀=450

Answer explanation

$2200 is invested at 5.5% p.a. compounded yearly. The amount of interest earned on the investment after 48 months, correct to the nearest cent, is

• 484

• 525.41

• 539.99

• 26 543.57

Answer explanation

What is the difference in money terms between investing  $100000 at 10% p.a. for 5 years compounded yearly as compared to compounded monthly? (Give the closest answer.)

• $3000

• $3500

• $4000

• $4500

Answer explanation

The number of interest-bearing periods for an investment that is compounded quarterly over 5 years is

• 5

• 60

• 59

• 20

Answer explanation

Four quarters per year over five years, thus 20 periods.

The future value, correct to the nearest cent, of $15 000 invested at 5.25% p.a. compounded monthly for 5 years is

• $15 331.01

• $18 937.50

• $19 373.22

• $19 491.48

Answer explanation

An investment of $1230 was made over 5 years at an interest rate of 6% p.a. with interest compounding annually. The interest earned during the second year is

• $1382.03

• $147.60

• $73.80

• $78.23

Answer explanation

Katya deposits $1000 into an account that adds 0.5% interest at the end of each month. Let 𝑀𝑛 be the money in the account at the end of month 𝑛. A first-order recurrence relation that would describe this situation is

• M_n+1 = 1.005M_n, M₀ = 1000

• M_n+1 = 1.05M_n, M₁ = 1000

• M_n+1 = M_n+50, M₀ = 1000

• M_n+1 = 1.005M_n, +1000 M₀

Answer explanation

If the effective annual interest rate for a loan with monthly repayments over 6 years is 7.2%  p.a., then the compound interest rate is closest to

• 7.44%

• 7.18%

• 6.97%

• 7.17%

Answer explanation

The minimum interest rate per annum required for an investment of  $5400 to grow to at least  $8000 in 3  years if compounded quarterly would be

• 3.33%

• 3.4%

• 8.67%

• 13.32%

Answer explanation

$900 is invested for 6½ years at 5.5% p.a. compounded monthly. The growth factor is given by

• r = (1 + 0.004 583)

• r = (1 + 0.004 583)^6.5

• r = (1 + 0.055)^9.5

• r = (1 + 0.004 583)⁷⁸

Answer explanation