24.3k views
5 votes
44. If an investment company pays 8% compounded quarterly, how much should you deposit now to have $6,000 (A) 3 years from now? (B) 6 years from now? 45. If an investment earns 9% compounded continuously, how much should you deposit now to have $25,000 (A) 36 months from now? (B) 9 years from now? 46. If an investment earns 12% compounded continuously. how much should you deposit now to have $4,800 (A) 48 months from now? (B) 7 years from now? 47. What is the annual percentage yield (APY) for money invested at an annual rate of (A) 3.9% compounded monthly? (B) 2.3% compounded quarterly? 48. What is the annual percentage yield (APY) for money invested at an annual rate of (A) 4.32% compounded monthly? (B) 4.31% compounded daily? 49. What is the annual percentage yield (APY) for money invested at an annual rate of (A) 5.15% compounded continuously? (B) 5.20% compounded semiannually? 50. What is the annual percentage yield (APY) for money invested at an annual rate of (A) 3.05% compounded quarterly? (B) 2.95% compounded continuously? 51. How long will it take $4,000 to grow to $9,000 if it is invested at 7% compounded monthly? 52. How long will it take $5,000 to grow to $7,000 if it is invested at 6% compounded quarterly? 53. How long will it take $6,000 to grow to $8,600 if it is invested at 9.6% compounded continuously?

User Phiver
by
8.3k points

1 Answer

3 votes

44. A:

A = P(1 + r/n)^(n*t)

(A) To have $6,000 in 3 years from now:

A = $6,000

r = 8% = 0.08

n = 4 (compounded quarterly)

t = 3 years

$6,000 = P(1 + 0.08/4)^(4*3)

$4,473.10

44. B:

________________________________________________

Using the same formula:

$6,000 = P(1 + 0.08/4)^(4*6)

$3,864.12

45. A:

A = P * e^(r*t)

(A) To have $25,000 in 36 months from now:

A = $25,000

r = 9% = 0.09

t = 36 months / 12 = 3 years

$25,000 = P * e^(0.09*3)

$19,033.56

45. B:

Using the same formula:

$25,000 = P * e^(0.09*9)

$8,826.11

__________________________________________________

46. A:

A = P * e^(r*t)

(A) To have $4,800 in 48 months from now:

A = $4,800

r = 12% = 0.12

t = 48 months / 12 = 4 years

$4,800 = P * e^(0.12*4)

$2,737.42

46. B:

Using the same formula:

$4,800 = P * e^(0.12*7)

$1,914.47

__________________________________________________

47. A:

For an investment at an annual rate of 3.9% compounded monthly:

The periodic interest rate (r) is the annual interest rate (3.9%) divided by the number of compounding periods per year (12 months):

r = 3.9% / 12 = 0.325%

APY = (1 + r)^n - 1

r is the periodic interest rate (0.325% in decimal form)

n is the number of compounding periods per year (12)

APY = (1 + 0.00325)^12 - 1

4.003%

47. B:

The periodic interest rate (r) is the annual interest rate (2.3%) divided by the number of compounding periods per year (4 quarters):

r = 2.3% / 4 = 0.575%

Using the same APY formula:

APY = (1 + 0.00575)^4 - 1

2.329%

__________________________________________________

48. A.

The periodic interest rate (r) is the annual interest rate (4.32%) divided by the number of compounding periods per year (12 months):

r = 4.32% / 12 = 0.36%

Again using APY like above:

APY = (1 + (r/n))^n - 1

APY = (1 + 0.0036)^12 - 1

4.4037%

48. B:

The periodic interest rate (r) is the annual interest rate (4.31%) divided by the number of compounding periods per year (365 days):

r = 4.31% / 365 = 0.0118%

APY = (1 + 0.000118)^365 - 1

4.4061%

_________________________________________________

49. A:

The periodic interest rate (r) is equal to the annual interest rate (5.15%):

r = 5.15%

Using APY yet again:

APY = (1 + 0.0515/1)^1 - 1

5.26%

49. B:

The periodic interest rate (r) is the annual interest rate (5.20%) divided by the number of compounding periods per year (2 semiannual periods):

r = 5.20% / 2 = 2.60%

Again:

APY = (1 + 0.026/2)^2 - 1

5.31%

____________________________________________________

50. A:

AHHHH So many APY questions :(, here we go again...

The periodic interest rate (r) is the annual interest rate (3.05%) divided by the number of compounding periods per year (4 quarterly periods):

r = 3.05% / 4 = 0.7625%

APY = (1 + 0.007625/4)^4 - 1

3.08%

50. B:

The periodic interest rate (r) is equal to the annual interest rate (2.95%):

r = 2.95%

APY = (1 + 0.0295/1)^1 - 1

2.98%

_______________________________________________

51.

We use the formula from while ago...

A = P(1 + r/n)^(nt)

P = $4,000

A = $9,000

r = 7% = 0.07 (annual interest rate)

n = 12 (compounded monthly)

$9,000 = $4,000(1 + 0.07/12)^(12t)

7.49 years

_________________________________________________

52.

Same formula...

A = P(1 + r/n)^(nt)

$7,000 = $5,000(1 + 0.06/4)^(4t)

5.28 years

_____________________________________________

53.

Using the formula:

A = P * e^(rt)

A is the final amount

P is the initial principal (investment)

r is the annual interest rate (expressed as a decimal)

t is the time in years

e is the base of the natural logarithm

P = $6,000

A = $8,600

r = 9.6% = 0.096 (annual interest rate)

$8,600 = $6,000 * e^(0.096t)

4.989 years

_____________________________________

Hope this helps.

User Stonedauwg
by
8.2k points

No related questions found