If $1200 is borrowed at 9% interest, find the amounts due at the end of 4 years if the interest is compounded as follows. (Round your answers to the nearest cent.) (i) annually $ 1693.9 Correct: Your answer is correct. (ii) quarterly $ 1204.3 Incorrect: Your answer is incorrect. (iii) monthly $ (iv) weekly $ (v) daily $ (vi) hourly $ (vii) continuously $

Answer and Explanation:

(i) The computation of compound interest for annual is shown below:-

Compound interest = A = P × (1 + r ÷ n)^t

= $1,200 × (1 + 9% ÷ 1)^1 × 4

= $1,200 × (1.09)^4

= $1,693.897932

or

= $1,693.90

(ii) The computation of compound interest for quarterly is shown below:-

= $1,200 × (1 + 9% ÷ 4)^4 × 4

= $1,200 × (1.09)^16

= $1,713.145749

or

= $1,713.15

Since it is quarterly so we divide the interest rate by 4 and multiply the time period by 4

(iii) The computation of compound interest for monthly is shown below:-

= $1,200 × (1 + 9% ÷ 12)^4 × 12

=  $1,200 × (1.0075)^48

= $1,717.6864

or

= $1,717.69

Since it is monthly so we divide the interest rate by 12 and multiply the time period by 12

(iv) The computation of compound interest for weekly is shown below:-

= $1,200 × (1 + 9% ÷ 52)^4 × 52

= $1,200 × (1.432883461 )^208

= $1719.460154

or

= $1,719.46

Since it is weekly so we divide the interest rate by 52 and multiply the time period by 52

(v) The computation of compound interest for daily is shown below:-

= $1,200 × (1 + 9% ÷ 365)^4 × 365

= $1,200 × (1.43326581  )^1460

= $1719.918972

or

= $1719.92

Since it is daily so we divide the interest rate by 365 and multiply the time period by 365

(vi) The computation of compound interest for hourly is shown below:-

= $1,200 × (1 + 9% ÷ 8760)^4 × 8760

= $1,200 × (1.433326764   )^35,040

= $1,719.992117

or

= $1719.99

(vii) The computation of compound interest for continuously is shown below:-

A = Pe^rt

= 1,200e^0.09 × 4

= 1,200e^0.36

= $1,720.00

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