Choose the best answer to the following question. Explain your reasoning with one or more complete sentences. The balance owed on your credit card doubles from\( \$ 2000 \)to\( \$ 4000 \)in\( 7 \)months. If your balance is growing exponentially, how much longer will it be until it reaches\( \$ 8000 \)?

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. It will be\( 7 \)months because the balance increases by\( \$ 4000 \)every three months.

B. It will be\( 21 \)months because\( \$ 2000 \)has to double three times to become\( \$ 8000 \).

C. It will be\( 14 \)months because the balance increases by\( \$ 3000 \)every\( 7 \)months.

D. It will be\( 7 \)months because the balance doubles every\( 7 \)months, and\( \$ 8000 \)is twice as much as\( \$ 4000 \).

E. It will be\( 14 \)months because it takes\( 7 \)months to reach\( \$ 4000 \)and another\( 7 \)months to reach\( \$ 8000 \).

F. It will be\( 21 \)months because the balance increases by\( \$ 2000 \)every\( 7 \)months, and\( \$ 8000 \)is\( \$ 6000 \)more than\( \$ 2000 \).

Use PMT\(= \frac { P ( \frac { r } { n } ) } { [ 1 - ( 1 + \frac { r } { n } ) ^ { - n t } ] } \)to delermine the regular payment amount, rounded to the nearest dollar. The price of a small cabin is $400,000 . The bank requires a 5% down payment. The buyer is offered two mortgage options: 20 -year fixed at 10%. Calculate the amount of inlerest paid for each option. How much does the buyer save in interest with or 30 -year fixed at 10% . the 20 -year option?

Find the monthly payment for the 20 -year option.

\(\$ \square \)

(Round to the nearest dollar as needed.)

Use PMT\( = \frac { P ( \frac { r } { n } ) } { [ 1 - ( 1 + \frac { r } { n } ) ^ { - n t } ] } \)to determine the regular payment amount, rounded to the nearest dollar. The price of a small cabin is\( \$ 40,000 \). The bank requires a\( 5 \% \)down payment. The buyer is offered two mortgage options:\( 20 \)-year fixed at\( 10 \% \)or\( 30 \)-year fixed at\( 10 \% \). Calculate the amount of interest paid for each option. How much does the buyer save in interest with the\( 20 \)-year option?

Calculate the total cost of interest for both mortgage options. How much does the buyer save in interest with the\( 20 \)-year option?

\( \$ \square \)

In terms of paying less in interest, which is more economical for a $110,000 mortgage: a 30 -year fixed-rate at 9.5% or a 15 -year fixed-rate at 9%? How much is saved in interest? Use the following formula to determine the regular payment amount.

PMT\( = \frac { P ( \frac { r } { n } ) } { [ 1 - ( 1 + \frac { r } { n } ) ^ { - n t } ] } \)

A. The 30 -year 9.5% loan is more economical. The buyer will save approximately\( \$ \square \)in interest.

B. The 15-year 9% loan is more economical. The buyer will save approximately\( \$ \square \)in interest.

Find the future value and interest earned if $8804.56is invested for 8 years at 6% compounded (a) semiannually and (b) continuously.

(a) The future value when interest is compounded semiannually is approximately\( \$ \square \).

(Type an integer or decimal rounded to the nearest hundredth as needed.)

The interest earned is approximately\( \$ \square \).

(Type an integer or decimal rounded to the nearest hundredth as needed.)

(b) The future value when interest is compounded continuously is approximately\( \$ \square \).

(Type an integer or decimal rounded to the nearest hundredth as needed.)

The interest earned is approximately\( \$ \square \).

(Type an integer or decimal rounded to the nearest hundredth as needed.)