Rita's Bank Account

Good start with I = prt. Now you need to know what P, R and T mean. Once you have that, you can calculate interest earned. The final answer is the initial amount plus the interest.

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Good start with I = prt. Now you need to know what P, R and T mean. Once you have that, you can calculate interest earned. The final answer is the initial amount plus the interest.

p = principal
r = rate = percent
t = time in terms of years (in this case)

rate = 6% = 0.06 in decimal form, right?

I = $84(0.06) (4 years), right?

I = 20.16

Then 20.16 + $84, right?

I get $104.16 but this is not the correct answer in the book. Book's answer is: $106.05. How do I get $106.05?


Rita banked $84 in her bank. She earned that money through summer work. The money was deposited at the begining of an interest period at a simple rate of 6%. If Rita left her money in the bank for 4 years, how much would she have in her account of the end of that period?

The book is compounding the interest from each year over the four years.

Rita has P0 ($84) dollars at the beginning of the first year. Use I=P0R*1 for the interest in the first year.

so at the beginning of the second year (end of the first) Rita has

P1=P0+P0R=P0(1+R)

the beginning of the third year (end of the second) Rita gets P1R*1 in interest and has

P2=P1+P1R=P1(1+R)=P0(1+R)(1+R)=P0(1+R)^2
See a pattern? At the end of the second year Rita's $84 dollars has grown by a factor of (1+R) squared (2)

Sure enough I can show at the end of the third year Rita has
P3=P0(1+R)^3
and the fourth
P4=P0(1+R)^4

this is called annual compounding of interest. For a year the interest is simple, and each year the interest is combined with the principal and used for the next years interest.

I checked P4=$84(1+.06)^4=$106.05 rounded to the nearest cent.

Rap c∫;?/

WOW
I thank you for your ongoing reply to my questions. I learning so much math through your notes.