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 NO LINKS!! (NOT MULTIPLE CHOICE)Use the formula A = P( 1 + r/n)^(nt) to calculate the balance A of an investment (in dollars) when P = $4000, r = 4%, and t= 10years, and compunding...
 meredith48034
 5 months ago
 Mathematics
NO LINKS!! (NOT MULTIPLE CHOICE)
Use the formula A = P( 1 + r/n)^(nt) to calculate the balance A of an investment (in dollars) when P = $4000, r = 4%, and t= 10years, and compunding is done by the day, by the hour, by the minute, and by the second. (Round your answers to the nearest cent).
a. compounding by the day: A= $
b. compounding by the hour: A= $
c. compounding by the minute: A= $
d. compounding by the second: A= $
Does increasing the number of compoundings per year result in unlimited growth of the balance? yes or no (choose one)

1 Answers
Answer:
a. compounding by the day: A = $5967.17
b. compounding by the hour: A = $5967.29
c. compounding by the minute: A = $5967.30
d. compounding by the second: A = $5967.30
Stepbystep explanation:
Part (a)
If the interest is compounding by the day then n = 365.
Given:
 P = $4000
 r = 4% = 0.04
 n = 365
 t = 10 years
Substitute the values into the compound interest formula and solve for A:
Part (b)
If the interest is compounding by the hour then:
 n = 365 × 24 = 8760
Given:
 P = $4000
 r = 4% = 0.04
 n = 8760
 t = 10 years
Substitute the values into the compound interest formula and solve for A:
Part (c)
If the interest is compounding by the minute then:
 n = 365 × 24 × 60 = 525600
Given:
 P = $4000
 r = 4% = 0.04
 n = 525600
 t = 10 years
Substitute the values into the compound interest formula and solve for A:
Part (d)
If the interest is compounding by the second then:
 n = 365 × 24 × 60 × 60 = 31536000
Given:
 P = $4000
 r = 4% = 0.04
 n = 31536000
 t = 10 years
Substitute the values into the compound interest formula and solve for A:
The more compounding periods throughout the year, the higher the future value of the investment. However, the difference between compounding by the day and compounding by the second results in a difference of 13 cents over the year, which is negligible comparatively.