 Sangeetha Pulapaka
1

# A savings account pays a 3% nominal annual interest rate and has a balance of $1,000. Any interest earned is # deposited into the account and no further deposits or # withdrawals are made. # Write an expression that represents the balance in one # year if interest is compounded annually. The compound interest formula is given by, A\ =\ P\left(\ 1+\frac{r}{n}\right)^{nt} where P is the initial amount which is$1000, the rate of interest is 0.03, n = 1 (since the interest is compounded once a year, annually), t = 1 year,

Plug in these find A=1000(1+0.03)\ =\ 1030

So, the balance in one year, of compounded annually is \$1030 Mahesh Godavarti
0

This is the case of compound interest since the interest is deposited back into the and no further deposits or withdrawals are made.

P(1) = Principal after 1 year = P(0) + interest after one year = P(0) + r P(0) = (1 + r) P(0)

P(2) = Principal after 2 years = P(1) + interest after second year = P(1) + r P(1) = (1 + r) P(1) = (1 + r)^2 P(0).

So, the amount after t years = 1000 (1 + 0.03)^t = 1000 x 1.03^t.