# Compound interest with duration less than compoundings in a year

I have the following problem:
How much do you have at the end if

a)You invest $8100\$8100 for 33 quarters at a yearly nominal interest rate of 16.916.9%?

b)You invest $8910\$8910 at a nominal yearly interest rate of 11.311.3% for 1414 weeks?

My solutions for those:

a) A=8100×(1+(0.169)×(34))34=8858.41A=8100 \times (1+(0.169)\times(\frac{3}{4}))^\frac{3}{4}=8858.41

b) A=8910×(1+(0.113)(1452))1452=8982.18A=8910 \times (1+(0.113)(\frac{14}{52}))^\frac{14}{52} =8982.18

Are those solutions correct? I don’t understand why the durations are less than the compounding period that my exponents become less than 1? In addition, “nominal interest rate” is the “compound interest”, right? Since we do not consider the inflation rate in the class.

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I am now thinking that I should use simple interest formula to solve it. Any ideas?
– Ninja
9 hours ago

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