Answer to Question #127502 in Microeconomics for fariza

Question

1.1) You lend a friend RM20,000 for a year. At the end of the year your friend agrees to pay you RM21,100. The interest rate on this loan is _______

Working Calculation:

1.2) You lend a friend RM20,000 for a year at an annual interest rate of 5%. At the end of the year your friend must pay you ________ in interest.

Working Calculation:

1.3) You agree to lend ________ to a friend for a year at an annual interest rate of 10%. At the end of the year your friend pays you RM600 in interest.

Working Calculation:

Answer 1

1.1) The interest rate on this loan is 5.5%

Working calculation:

$A=P(1+r)^{t}$

$RM21,100=RM20,000(1+r)^{1}$

$\frac{RM21,100}{RM20,000}=\frac{RM20,000}{RM20,000}(1+r)$

$1.055=1+r$

$r=1.055-1$

$r=0.055\times100$

$r=5.5\%$

1.2) The interest amount is RM 1,000

Working calculation:

$A=P(1+r)^{1}-P$

$RM20,000(1+0.05)-RM20,000$

$(RM20,000\times1.05)-RM20,000$

$RM21,000-RM20,000$

$Interest=RM1,000$

1.3) The amount lend will be RM 6,000

Working calculation:

$Interest=A-P$

$If 10\%=RM600=Interest$

$P=100\%=?$

$Therefore P=\frac{100\%}{10\%}\times RM600$

$P=RM6,000$

Test to confirm the answer:

$A=P(1+r)^{1}-P$

$RM6,000(1+0.1)^{1}-RM6,000$

$(RM6,000\times1.1)-RM6,000$

$RM6,600-RM6,000$

$Interest\; amount=RM600$