A bank offers an investment account with an annual interest rate of
1.31%
compounded annually. Hans invests
$3600
into the account for
3
years.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas
.
(a) Assuming no withdrawals are made, how much money is in Hans' account after
3
years?
$
(b) How much interest is earned on Hans' investment after
3
years?
(a) Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the initial investment, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Plugging in the given values:
A = 3600(1 + 0.0131/1)^(1*3) = $3,809.03
Therefore, Hans has $3,809.03 in his account after 3 years.
(b) To find the amount of interest earned, we subtract the initial investment from the final amount:
Interest = A - P = $3,809.03 - $3,600 = $209.03
Therefore, Hans earned $209.03 in interest over 3 years.
To calculate the amount of money in Hans' account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money in the account
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
Given:
P = $3600
r = 1.31% = 0.0131 (in decimal form)
n = 1 (since interest is compounded annually)
t = 3 years
(a) Plugging in the values into the formula:
A = 3600(1 + 0.0131/1)^(1*3)
A = 3600(1.0131)^3
A ≈ $3743.46
After 3 years, the amount of money in Hans' account would be approximately $3743.46.
(b) To calculate the interest earned on Hans' investment, we subtract the principal amount from the final amount:
Interest = A - P
Interest = $3743.46 - $3600
Interest ≈ $143.46
Hans would earn approximately $143.46 in interest on his investment after 3 years.