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Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 100 into his bank account, and Robbie deposits 50 into his. Interest is credited to each account at a discount rate of d. The amount of interest earned in Bruce’s account during the 11th year is equal to X. The amount of interest earned in Robbie’s account during the 17th year is also equal to X. Calculate X.
I know the answer in 38.9, I just can't remember how to get there .... Thanks!
Cool question.Quote:
Originally Posted by jlt1209
Bruce's interest earned between t=10 and t=11 is equal to Robbie's interest earned between t=16 and t=17, so we can write
100(1+r)^11 - 100(1+r)^10 = 50(1+r)^17 - 100(1+r)^16
We need some common terms, so rewrite as
100(1+r)^10(1+r) - 100(1+r)^10 = 50(1+r)^16(1+r) - 100(1+r)^16
Pull some terms out to get
100(1+r)^10((1+r) - 1) = 50(1+r)^16((1+r) - 1)
Hmm, delicious
2(1+r)^10((1+r) - 1) = (1+r)^16((1+r) - 1)
2(1+r)^10/((1+r)^16) = ((1+r) - 1)/((1+r) - 1)
Shaping up!
2(1+r)^10/((1+r)^16) = 1
2/((1+r)^6) = 1
2 = (1+r)^6
2^(1/6) = 1+r
1.12246 = 1+r
r = 0.12246
Now that we've got r, just plug it into one side of
100(1+r)^11 - 100(1+r)^10 = 50(1+r)^17 - 100(1+r)^16
to find X.
100(1+0.12246)^11 - 100(1+0.12246)^10 = 38.87792
ROCK AND ROLL!
ORQuote:
Originally Posted by jlt1209
If d is the effective discount rate, then
^{ - 11} - 100\left( {1 - d} \right)^{ - 10} = 50\left( {1 - d} \right)^{ - 17} - 50\left( {1 - d} \right)^{ - 16} <br />
)
which then implies that
Thanks my ass! Judging by the lack of any kind of work you've shown so far, seems more like you've never been there at all and just want others to do your work for you.Quote:
Originally Posted by jlt1209