4. Joe deposits $2,000 into a savings account. The account compounds his money quarterly at a rate of 4%. a) How much money does Joe have after a year? Round your answer to the nearest ten cents. b) After 18 months? Round your answer to the nearest dollar. c) When will his account grow to $25,000? Round your answer to the nearest year.

Step-by-step explanation:

Formula to be used,

Final amount =

r = rate of interest

n = number of compounding in a year

t = Duration of investment in years

Initial amount = $2000

r = 4% = 0.04

n = 4

A). Final amount =

                           = 2000(1.01)⁴

                           = 2081.21

                           ≈ $2081

B). If t = 18 months ≈ 1.5 years

    Final amount =

                           =

                           = 2123.04

                           ≈ $2123

C). If final amount = $25000

     25000 =

     12.5 =

     log(12.5) =

     log(12.5) = t[log(1.040604)]

     t =

       = 63.458

       ≈ 64 years

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step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47