Question

1.Find the amount in an account where $200 is invested at 3.5% compounded quarterly for a period of 3 years.

2.Find the amount in an account where $200 is invested at 3.5% compounded continuously for a period of 3 years.

Each answer must include the intermediate steps used to arrive at the answer.

Answer 1

Part 1 :

P = $200

r = 3.5% or 0.035

t = 3

n = 4

Compound interest formula =
`P(1+(r)/(n))^(nt)`

=
`200(1+(0.035)/(4))^(3*4)`

=
`200(1.00875)^(12)`

=
`200*1.1102`

= 222.04

So, money in the bank will be = 200+222.04 = $422.04

Part 2 :

P = $200

r = 3.5% or 0.035

t = 3

Continuous compound interest formula is =

A =
`Pe^(rt)`

Putting e = 2.71828 we get.

A =
`200(2.71828)^(0.035*3)`

=
`200(2.71828)^(0.105)`

= 200*1.11071 = 222.14

Hence, amount in account after 3 years will be= 200+222.14 = $422.14