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4 years ago

Angles A and B are supplementary. If angle A= 137° then angle B is

Mathematics

1 answer:

maksim [4K]4 years ago

5 0

Answer:

43°

Step-by-step explanation:

Angles A and B are supplementary

i. e. angle A + angle B =180°

137° + angle B =180°

angle B=180°-137°

=43°

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Fofino [41]

-2(x + 3) = -2(x + 1) - 4

-2x - 6 = -2x - 2 - 4 distributed -2 on the left and on the right

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-6 = -6

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8 0

4 years ago

5.Richard Miyashiro purchased a condominium and obtained a 30-year loan of $196,000 at an annual interest rate of 8.20%. (Round

GREYUIT [131]

Answer:

5 a) PMT=$1,465.60

b) Total Payments=$527,616

c) Total Interest=$331,616

6a) Interest=$1,079.93

b) Principal=$584.07

Step-by-step explanation:

a. Given the loan amount is $196,000, annual rate is 8.2% and the loan term is 30 years.

-The monthly mortgage payment can be calculated as follows:

$PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})$

Where:

PMT is the monthly mortgage payment
r is the annual interest rate
n,t is the number of annual payments and time in years respectively

-We substitute to solve for PMT:

$PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})\\\\=196000[\frac{(0.082/12)}{1-(1+\frac{0.082}{12})^{-12\times30}}]\\\\=\$1,465.60$

Hence, the monthly mortgage payment is $1,465.60

b. The total number of payments is obtained by multiplying the total number of payments by the amount of each payment:

$\sum(payments)=PMT\times nt\\\\=1465.60\times 12\times 30\\\\=\$527,616.00$

Hence, the total amount of payments is $527,616

c. The amount of interest paid over the loan's term is obtained by subtracting the principal loan amount from the total payments made:

$Interest=Payments-Principal\\\\=527,616.00-196,000.00\\\\=\$331,616$

Hence, an interest amount of $331,616 is paid over the loan's term.

6 a) We first obtain the effective loan amount by subtracting the down-payment:

$Loan \ Amount= Regular \ Price -Downpayment\\\\=205700-0.1(205700)\\\\=\$185,130$

The interest paid on the first mortgage payment is calculated as below:

$I=\frac{r}{n}\times P\\\\I=Interest\\r=interest \ rate\\n=Payments \ per \ year\\P=Outstanding \ loan \ balance\\\\\therefore I=\frac{0.07}{12}\times 185130\\\\=\$1,079.93$

Hence, the amount of interest in the first payment is $1,079.93

b. The amount of principal repaid is obtained by subtracting the interest amount from the monthly mortgage payments;

$Principal \ Paid=PMT-Interest\\\\PMT=A[\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}}]\\\\=185130[\frac{(0.07/12)}{1-(1+\frac{0.07}{12})^{-180}}\\\\=1664.00\\\\\\Principal \ Paid=1664.00-1079.93\\\\=\$584.07$