# Math

Ginny Katz has decided to invest \$700 quarterly for 10 years in an ordinary annuity at 8 percent. The total cash value of the annuity at end of year 10 is?

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1. i = .08/4 = .02
n = 10(4) = 40

amount = 700( 1.02)^ 40 - 1)/.02

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2. This Compound interest
using
Amount =
principle * ((Rate + 100)/100)^time

Here Rate is per time period
i.e 8% per annum will be 2% per quater
Time period is 10 years = 40 quater year
P=700 \$

Putting values
Amount = 700 * ((2+100)/100)^40
=700 * (51/50)^40
using scientific calculator
(51/50)^40 = 2.208

=700 * 2.208
=1545.6 \$ =7728/5 \$ (ans)

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700 (1.02^40 - 1)/.02 is \$42,281.39

Your solution makes no sense at all.
Even without any interest, there would be 40 payments of 700 for \$28,000

Unless you are sure of the math for compound interest, you are just confusing students more by giving them incorrect solutions.

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4. 700 \$ make 42281 \$ in ten years
Totally wrong this cant be true
He had invested money that will be get in a collection not in payment

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5. Fact:
quarterly deposits for 10 years ---> 40 payments
quarterly rate --- .08/2
standard formula that has been used for hundreds of years
Amount = deposit ( (1+i)^n - 1)/i , where i is the rate as a decimal and n is the number of payments or deposits

= 700( 1.02^40 - 1)/.02
= 42281.39

Fact:
my answer is right and you are wrong.
To convince yourself, complete the following table for 40 rows

time, deposit, interest on balance, increase in balance, balance
1 --- 700 ---0.00 ------------ 700.00 ---------- 700.00
2 --- 700 ---14.00------------714.00-----------1414.00
3 ----700 ---28.28------------728.28-----------2142.28
4 ----700 ---42.85 -----------742.85 -----------2885.13
........ that is at the end of the 1st year..........
etc.

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