Suppose Martina places $4000 in an account that pays 19% interest compounded each year.

Assume that no withdrawals are made from the account.

(a) Find the amount in the account at the end of 1 year.

(b) Find the amount in the account at the end of 2 years.

(a) $4760

(b) $5664.40

Step-by-step explanation:

Each year, the value in the account is multiplied by (1+r), where r is the annual interest rate.

(a) At the end of the first year, the account balance is ...

$4000*1.19 = $4760.00

(b) At the end of the second year, the account balance is ...

$4760.00*1.19 = $5664.40

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Comment on the general case

In general, after t years, the account balance for principal P will be ...

A = P (1 + r) ^t

If interest is compounded n times per year, the formula becomes ...

A = P (1 + r/n) ^ (nt)

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P (1 + r/n) ^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $4000

r = 19% = 19/100 = 0.19

n = 1 because it was compounded once in a year.

a) when t = 1 year

A = 4000 (1 + 0.19/1) ^1 * 1

A = 4000 (1.19)

A = $4760

b) when t = 2 years

A = 4000 (1.19) ^2

A = $5664.4