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Question 1170255: Nicole will be starting university next fall, she wishes to invest $7000.0 saved from her summer
job. Her bank offers 2.75% for a one-year term or 2.6% for 6 months and 2.9% for the second six
months. Which is the better method of investment, 1 year or 2 six month investments?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if she invests 7000 on a year term, she will have .....
7000 * 1.0275 ^ 1 = 7192.5 at the end of the 12 month investment.
if she invests 7000 on two half year terms, she will have.....
7000 * 1.026 ^ (1/2) = 7090.416067 at the end of the first 6 month investment.
she will then turn around and invest that amount for the second 6 months to get
7090.416067 * 1.029 ^ (1/2) = 7192.492336 at the end of the second 6 month investment.
7192.5 versus 7192.492336 favors the 12 year term investment.
the difference is very small though.
7192.5 minus 7192.492336 = .007664.
that's less than a penny difference.
the above does not assume monthly compounding of interest.
if you assume monthly compounding of interest, then:
if she invests 7000 on a one year term, she will have ....
7000 * (1 + .0275/12)^12 = 7194.944923 at the end of the 12 month term investment.
if she invests 7000 on two half year terms, she will have .....
7000 * (1 + .026/12) ^ 6 = 7091.494343 at the end of the first 6 month investment.
she will then turn around and invest that amount for the second 6 months to get
7091.494343 * (1 + .029/12) ^ 6 = 7194.944261 at the end of the second 6 month investment.
the difference is now 7194.944923 minus 7194.944261 = .006714..
that's still less than a penny, but the difference is smaller than without monthly compounding.
the difference is .007664 without monthly compounding and .006714 with monthly compounding.
in either case, the difference is still less than a penny.
she could do it either way and be fine with either of them, however, it's simpler to just go with the 12 month investment.
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