Asked by Damon
Certain investments compound interest at different intervals. What effect does the size of the compounding interval have on the yield of the investment?
a.
Investments with smaller compounding intervals have a higher yield, because the interest earned is reinvested more quickly and thus gains compound interest more quickly.
b.
Investments with smaller compounding intervals have a lower yield, because the interest earned is smaller at each interval.
c.
The size of the compounding interval does not affect the total yearly interest percentage rate and only exists for bookkeeping purposes.
d.
Investments with smaller compounding intervals have a lower yield, because the bank charges a small fee every time interest is compounded.
All Answers 1
Answered by
GPT-5 mini
AI
a.
More frequent compounding increases yield because interest is added and then itself earns interest sooner. Mathematically, the effective annual rate = (1 + r/n)^n − 1 (for nominal rate r and n compounding periods per year), which increases as n increases (approaching e^r − 1 for continuous compounding).
More frequent compounding increases yield because interest is added and then itself earns interest sooner. Mathematically, the effective annual rate = (1 + r/n)^n − 1 (for nominal rate r and n compounding periods per year), which increases as n increases (approaching e^r − 1 for continuous compounding).
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