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Helpp !! C2 question on geometric

HEY :P

Ginny opens a savings account and decides to pay £200 into the account at the start of
each month. At the end of each month, interest of 0.5% is paid into the account.
a Find, to the nearest penny, the interest paid into the account at the end of the
third month. (4)

amount in account after the 3rd payment in
=200+(1.005x200)+(1.005^2 x200)
=603.005
interest paid at end of 3rd month
=0.005x603.005=£3.02 (nearest penny)

i dont get why they did 603.005 x 0.005 ? could someone explain this to me .

thank you , would appreciate it
Original post by Sadilla
HEY :P

Ginny opens a savings account and decides to pay £200 into the account at the start of
each month. At the end of each month, interest of 0.5% is paid into the account.
a Find, to the nearest penny, the interest paid into the account at the end of the
third month. (4)

amount in account after the 3rd payment in
=200+(1.005x200)+(1.005^2 x200)
=603.005
interest paid at end of 3rd month
=0.005x603.005=£3.02 (nearest penny)

i dont get why they did 603.005 x 0.005 ? could someone explain this to me .

thank you , would appreciate it


At the end of the 1st month you put in 0.0052000.005\cdot 200 so that in total you have 200+0.005200=2001.005200+0.005\cdot 200 = 200 \cdot 1.005.

Similarly, the end of the 2nd month you put in 0.005(2001.005)0.005 \cdot (200 \cdot 1.005) so that you end up with 2001.005+0.005(2001.005)=2001.0052200 \cdot 1.005 + 0.005 \cdot (200 \cdot 1.005) = 200 \cdot 1.005^2

So it should be clear why they did what they did for the end of the 3rd month.

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