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3 November, 20:39

You want to buy a camera, but you are $1000 short. Your favorite uncle, offers to lend you that money, if you pay him $1,200 two years from today. He compounds interest monthly. A greedy high school friend also offers to give you the money. However, she says there is going to be a loan processing fee of $20 that will be included in the loan amount (once you pay the processing fee, she lends you $1020). Your greedy friend is expecting to receive $1220 in two years, based on monthly compounding of interest.

(a) What is the monthly rate your favorite uncle is charging? What rate is your greedy friend charging?

(b) What effective annual rate are your favorite uncle and your greedy friend charging?

(c) Which one would you prefer to borrow from?

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  1. 3 November, 21:07
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    Future value after 24 months = 1200

    present value = 1000

    Let monthly rate of interest = r

    1000 = 1200 / (1+r) ²⁴

    (1+r) ²⁴ = 1200/1000

    (1+r) ²⁴ = 1.2

    taking log on both sides

    24 log (1+r) = log 1.2

    24 log (1+r) =.07918

    log (1+r) =.003299

    (1+r) = 1.007625

    r =.007625

    monthly rate of interest in percent =.7625%

    II Option

    Future value after 24 months = 1220

    present value = 1020 - 20 = 1000

    Let monthly rate of interest = r

    1000 = 1220 / (1+r) ²⁴

    (1+r) ²⁴ = 1220/1000

    (1+r) ²⁴ = 1.22

    taking log on both sides

    24 log (1+r) = log 1.22

    24 log (1+r) =.086359

    log (1+r) =.003598

    (1+r) = 1.008319

    r =.008319

    monthly rate of interest in percent =.8319%

    b)

    Effective annual rate of uncle = (1.007625) ¹² - 1

    = 1.09543 - 1 =.09543

    In percent = 9.543 %

    Effective annual rate of greedy friend = (1.008319) ¹² - 1

    = 1.1045 - 1

    = 10.45 %

    c) The first one is cheaper so it is preferable.
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