Find Difference in Total Cost for Engagement Ring at 2 Jewelers

[bergausstein]

1. A prospective bridegroom wants to buy an engagement
ring. Two jewelry stores each show him a ring at a cost
of \$2400. One jeweler requires a 20% down payment
with the balance to be paid at the end of one year at 11%
simple interest. The other jeweler requires a 25% down
payment with the balance to be paid at the end of one
year at 12% simple interest. What is the difference in
total cost?

my solution,

for the first jeweler

$.20(2400)=480$ \$480 down payment

$2400-480=1920$ \$1920 balance to be paid(with 11% interest)

then the total cost is,

$1920(.11)+1920+480=2611.2$

\$ 2611.2 total cost of the ring at the first jewelry store.

for the 2nd jewelry store,

$.25(2400)=600$ \$600 down payment

$2400-600=1800$ \$1800 balance to be paid(with 12% interest)

then the total cost is,

$1800(.12)+1800+600=2616$

\$ 2616 total cost of the ring at the 2nd jewelry store.

so, $2616-2611.2=4.8$ \$4.8 is the difference in the total cost.

did i get it correctly?

2. Because payment is one month overdue, a customer
receives a department store bill for \$332.92 that includes
a 1.5% interest charge for late payment. What was the
original amount of the bill?

my solution

$332.92-332.92(0.015)=327.9262$

\$327.9262 original price.

is this also right?

thanks!

 

[mente oscura]

1. A prospective bridegroom wants to buy an engagement
ring. Two jewelry stores each show him a ring at a cost
of \$2400. One jeweler requires a 20% down payment
with the balance to be paid at the end of one year at 11%
simple interest. The other jeweler requires a 25% down
payment with the balance to be paid at the end of one
year at 12% simple interest. What is the difference in
total cost?

my solution,

for the first jeweler

$.20(2400)=480$ \$480 down payment

$2400-480=1920$ \$1920 balance to be paid(with 11% interest)

then the total cost is,

$1920(.11)+1920+480=2611.2$

\$ 2611.2 total cost of the ring at the first jewelry store.

for the 2nd jewelry store,

$.25(2400)=600$ \$600 down payment

$2400-600=1800$ \$1800 balance to be paid(with 12% interest)

then the total cost is,

$1800(.12)+1800+600=2616$

\$ 2616 total cost of the ring at the 2nd jewelry store.

so, $2616-2611.2=4.8$ \$4.8 is the difference in the total cost.

did i get it correctly?

Hello.

Yes.

2. Because payment is one month overdue, a customer
receives a department store bill for \$332.92 that includes
a 1.5% interest charge for late payment. What was the
original amount of the bill?

my solution

$332.92-332.92(0.015)=327.9262$

\$327.9262 original price.

is this also right?

thanks!

Not.

Supposing that 1,50 % is the total interest for the month of delay:

P=original price

$$P+\dfrac{1.5}{100} P=1.015 \ P=332.92$$

$$P=\dfrac{332.92}{1.015}=328$$Checking:

$$328+328 \dfrac{1.5}{100}=328+4.92=332.92$$

Regards.