Question

Orca Research made an initial deposit into an account paying 2% compounded annually. Orca withdrew $2178 at the end of year 3 and made a deposit of $8390 at the end of year 7. By the end of year 13, Orca had $53867 in the account. What was Orca's initial deposit?

Answer 1

@DanJS

Answer 2

New answer P_o = 9415.38

Answer 3

@DanJS

Answer 4

Single payment compound interest?

Answer 5

i havent ever did this type

Answer 6

It's okay.

Answer 7

It's an engineering econ course

Answer 8

i would take the initial, compound it till the withdrawal, take the withdrawal off, then compound that till the deposit, then add that, then compound it till year 13

Answer 9

but there is prolly another way

Answer 10

can you show me the way you speak of?

Answer 11

P*(1.02)^3 - 2178 is up to end of year 3

Answer 12

then that amount is compounded for 4 years

[ P*(1.02)^3 - 2178] * (1.02)^4

Answer 13

1.02? you mean 0.02?

Answer 14

it increases by 2%, so you need

p*(1 + 0.02) --- P + 0.02P, or P*(1.02)

Answer 15

original P plus 2% of original

Answer 16

kk

Answer 17

P*(1.02)^3 to end of third year

P*(1.02)^3 - 2178 take the withdrawal off now

Answer 18

[ P*(1.02)^3 - 2178] * (1.02)^4 4 years of compounding that whole initial quantity

Answer 19

kk

Answer 20

[ P*(1.02)^3 - 2178] * (1.02)^4 + 8390 deposit

[ [ P*(1.02)^3 - 2178] * (1.02)^4 + 8390] * (1.02)^6 compound 6 more years all that

Answer 21

then that should be the final amount

[ [ P*(1.02)^3 - 2178] * (1.02)^4 + 8390] * (1.02)^6 = 53867

solve for P. lol

Answer 22

it shouold work, but maybe ill run it in a calc real fast

Answer 23

That makes a lot of sense. However, I believe you are right there is another way. we are using geomtric gradient formulas, arithmetic gradient, etc.

Answer 24

p=$36389.30

Answer 25

yeah, it probably is shown like i just did it, then tidied up with those formulas you have on those sheets

Answer 26

is there a way to check to see if that answer is correct?

Answer 27

yep it works.

Answer 28

lol really

Answer 29

plug p back into the equation

Answer 30

i just did a bunch of nested exponential functions, because of the inputs in the middle

Answer 31

it's a solution

Answer 32

oh i mean is it right, i think it might be

Answer 33

like i took the normal compunding to right before the withdrawal, then you have to begin using that entire quantity now to start the next years of compounding, exe...

Answer 34

well goodluck,

Answer 35

Thanks