Question

Your bank offers you a personal loan of $6000 at an interest rate of 6% compounded monthly. Calculate how long it would take for the debt to earn at least $895.89 of interest on the loan.

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Answer 1

Interest amount as per compound interest method is:

I = P x [(1+i) ⁿ -1]

I = Interest amount = $ 895.89

P = Principal of loan = $ 6,000

i = Periodic interest rate = 0.06/12 = 0.005 p.m.

n = Number of periods

$ 895.89 = $ 6,000 x [(1+0.005) ⁿ -1]

= $ 6,000 x [(1.005) ⁿ -1]

(1.005) ⁿ -1 = $ 895.89/$ 6,000

(1.005) ⁿ = 0.149315 + 1

(1.005) ⁿ = 1.149315

Taking log of both sides and solving for n, we get:

n x log 1.005 = log 1.149315

n = log 1.149315/log 1.005

n = 0.060439074827/0.0021660617565

   = 27.90274776 or 27.90

Number of years = 27.90/12 = 2.33 years

The loan will take 2.33 years to earn interest of $ 895.89