Answer:
(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)
Answer:
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
