(ii)

(iii)

(ii)

(ii)

(iii) The term 5000 × 1.0025⁶ means the value of the loan would have risen by a factor of 1.0025⁶ had there been no repayments.

(iv) Milka paid 44 months @ $121.35 pm = $5,339.40.

Hence total interest = $339.40.

(ii)

(iii)

The monthly interest is 1% - so rate is 1.01.
Let the amount of the monthly repayment be R.

At the end of month 1, the balance is the $1,500 less the repayment.

∴ A₁ = 1500 - R

A₂ = 1500 - 2R

A₃ = 1500 - 3R

For the next payment, the interest starts to be charged and it is calculated on the balance of the loan - so here on $(1500-3R).

A₄ = (1500 - 3R) × 1.01 - R

A₅ = [(1500 - 3R) × 1.01 - R] × 1.01 - R

= (1500 - 3R) × 1.01² - R - 1.01R

A₆ = [(1500 - 3R) × 1.01² - R - 1.01R] × 1.01 - R

= (1500 - 3R) × 1.01³ - R(1 + 1.01 + 1.01²)

The month number is 6 and the index in the first term on the right is 3 and there are 3 terms in the series. So a three difference (only 33 terms in the series).

The loan went for 36 months.

∴ A₃₆ = (1500 - 3R) × 1.01³³ + R × .

At the end of 36 months, there is a zero balance (A₃₆ = 0).

Rearranging we get

R = $48.40

(ii) $48.40 × 36 = $1,742.40

So $242.40 in interest.

(ii)

(iii)

(ii)

(iii)

(ii)

(iii)

n = 60; r = 8% ÷ 12 = 0.0067.

End M1 = 5500 × 1.0067 - R

End M2 = (5500 × 1.0067 - R) × 1.0067 - R

= 5500 × 1.0067² - R - 1.0067R

End M3 = (5500 × 1.0067² - R - 1.0067R) × 1.0067 - R

= 5500 × 1.0067³ - R - R1.0067 - R1.0067²

= 5500 × 1.0067³ - R(1 + 1.0067 + 1.0067²)

M60 = 5500 × 1.0067⁶⁰ - R × .

R = $111.63

(ii) First calculate Ruby's balance at the end of Month 3 using the calculated value for R:

Balance = $5,274.15.

This makes the next calculations easier by not having to repeat the series from the beginning. Then calculate M4 and M5 by multiplying by the interest rate.

End M4 = 5274.15 × 1.0067

End M5 = 5274.15 × 1.0067² = 5,345.06

From M6 on, start a new series:

M6 = 5345.06 × 1.0067 - R

M7 = (5345.06 × 1.0067 - R)1.0067 - R

= 5345.06 × 1.0067² - R - 1.0067R

We can now form the usual series for the 55 months following the resumption of payments.

(ii) It is easier to do the next part if Matilda's amount owing at the end of her 3 months of non-payment is determined. Then a value can be used from which to build the next series.

End of 2 months, Matilda owes $3,860.40 (from M2 above).

After 3 more months with no payment, Matilda owes

3869.40 × 1.0075³ = $3,947.91

Let P be the new repayment amount:

(ii)

(iii)