Answer:
Explanation:
o calculate the total at the end of each year, we can use the formula for compound interest:
A=P(1+rn)n⋅tA=P(1+nr)n⋅t
where:
AA is the total amount at the end of the time period,
PP is the principal amount (initial deposit),
rr is the annual interest rate (expressed as a decimal),
nn is the number of times interest is compounded per year, and
tt is the number of years.
In this case:
P = $10
r=5%=0.05r=5%=0.05 (as a decimal, 5% is divided by 100)
n=1n=1 (interest is added once a year, annually)
Let's calculate the total at the end of each year:
Total at the end of year 1:
A1=10(1+0.051)1⋅1A1=10(1+10.05)1⋅1
A_1 = 10 \times 1.05 = $10.50
Total at the end of year 2:
A2=10.50(1+0.051)1⋅1A2=10.50(1+10.05)1⋅1
A_2 = 10.50 \times 1.05 = $11.03
Total at the end of year 3:
A3=11.03(1+0.051)1⋅1A3=11.03(1+10.05)1⋅1
A_3 = 11.03 \times 1.05 = $11.58
So, the amounts in the account at the end of each year will be:
Total at the end of year 1: $10.50
Total at the end of year 2: $11.03
Total at the end of year 3: $11.58