Question

A loan of $1400 is due in 1 year at a simple interest rate of 12%. Partial payments of $400 in 2 months, $25 in 6 months, and $700 in 8 months are made

A. Construct a timeline clearly showing the timing of the debt and all repayments.

B. Determine the balance due at the end of the 12 months using the merchant rule

C. Determine the balance due at the end of the 8 months using the declining balance method

Answer 1

A. 2 month - 400

6 month - 25

8 month - 700

12 month - 443

B. the merchant rule:

value of the debt at 12 month:

$S=1400\times(1+0.12\times\frac{12}{12})=1568$

$S2=400\times(1+0.12\times\frac{2}{12})=408$

$S6=25\times(1+0.12\times\frac{6}{12})=26.5$

$S8=700\times(1+0.12\times\frac{4}{12})=728$

1568-408-26.5-728=405.5

$S12=405.5\times(1+0.12\times\frac{12}{12})=454.16$

C. the declining balance method:

$I=P\times r\times T$

to month 2

$I=P\times r\times T=1400\times0.12\times\frac{2}{12}=28$

400>28, new balance 1400+28-400=1028

month 2 to month 6

$I=P\times r\times T=1028\times0.12\times\frac{4}{12}=41.12$

25<41.12, new balance 1028-41.12+25=1011.88

month 6 to month 8

$I=P\times r\times T=1011.88\times0.12\times\frac{2}{12}=20.24$

700>20.24 new balance 1011.88+20.24-700=332.12