Compound interest questions, grade 11 math.

  1. Write a sequence that represents the amount of money that will accumulate if $5000 is invested at 6% per year, compounded semi-annually. Determine tn. In this case, what does n represent?
  2. Write a sequence that represents the amount of money that will accumulate if $10 000 is invested at 8% per year, compounded quarterly. Determine tn. What does n represent?

  3. Write a sequence that represents the amount of money that will accumulate if the principal is P and the interest rate per year is r. Interest is compounded monthly. Determine tn. What does nrepresent?

  4. The compound interest formula is A = P(1 + i)n. Explain what APi, and n represent.
  5. Describe the relationship between the mathematics of calculating compound interest, and the mathematics behind analysing geometric sequences. How might compound interest be described as a problem of applied geometric sequences?

Expert Answers

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1. You should remember the formula of compound interest such that:

`A = P(1 + r/n)^(nt) `

A represents the amount of money accumulated

P represents the amount of money invested

t represents the number of years

n represents the number of times per year the interest is compounded

You need to substitute the given values in formula of compound interest such that:

`A = 5000(1 + 0.06/2)^(2t)`

`A = 5000*1.03^(2t)`

You may evaluate the amount of money accumulated after 1 year, two years, three years to write the geometric sequence `A_1,A_2,A_3` ,... such that:

`A_1 = 5000*1.03^2`

`A_2 =5000*1.03^4` 

`A_3 =5000*1.03^6`

............................

Hence, evaluating the geometric sequence, using the formula of compound interest, yields `5000*1.03^2 , 5000*1.03^4 , 5000*1.03^6,...`

2. You need to substitute the given values in formula of compound interest such that:

`A = 10000(1 + 0.08/4)^(4t)`

`A = 10000*1.02^(4t)`

You may evaluate the amount of money accumulated after 1 year, two years, three years to write the geometric sequence `A_1,A_2,A_2` ,... such that:

`A_1 = 10000*1.02^4`

`A_2 = 10000*1.02^8`

`A_3 =10000*1.02^12`

............................

Hence, evaluating the geometric sequence, using the formula of compound interest, yields `10000*1.02^4 ,10000*1.02^8 , 10000*1.02^12,....`

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