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2 years ago

2. Suppose you borrow $2,000 at 5% and you are going to make annual payments of $734.42. How long before you pay off the loan

Business

1 answer:

Alona [7]2 years ago

6 0

Answer:

3 years

Explanation:

The computation of the time period is shown below

Present value of annuity = Annuity × [1 - (1 + interest rate)^-time period] ÷ rate

$2,000 = $734.42 × [1 - (1.05)^-n] ÷ 0.05

$2,000 = $14,688.4 × [1-(1.05)^-n]

1-(1.05)^-n = ($2000 ÷ $14,688.4)

(1.05)^-n = 1 - ($2000 ÷ $14,688.4)

( 1 ÷ 1.05)^n = 0.86383813

Now take the log to the both sides

n × log(1 ÷ 1.05) = log0.86383813

n = log0.86383813 ÷ log (1 ÷ 1.05)

= 3 years

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