Math  /  Algebra

QuestionWhat is the balance after 2 years in a savings account with an initial investment of $1,250\$ 1,250 and a 5\% annual compound interest rate?

Studdy Solution

STEP 1

1. The initial investment in the savings account is P=$1250P = \$1250.
2. The annual interest rate is r=5%=0.05r = 5\% = 0.05.
3. The interest is compounded annually.
4. The duration for which the interest is calculated is t=2t = 2 years.

STEP 2

1. Identify the formula for compound interest.
2. Plug in the given values into the formula.
3. Calculate the balance after 2 years.

STEP 3

The formula for compound interest when compounded annually is:
A=P(1+rn)nt A = P \left(1 + \frac{r}{n}\right)^{nt}
Since the interest is compounded annually, n=1n = 1. Therefore, the formula simplifies to:
A=P(1+r)t A = P (1 + r)^t

STEP 4

Plug the given values into the formula:
P=1250,r=0.05,t=2 P = 1250, \quad r = 0.05, \quad t = 2
Thus, the balance after 2 years is:
A=1250(1+0.05)2 A = 1250 \left(1 + 0.05\right)^2

STEP 5

Simplify the expression inside the parentheses and then raise it to the power of 2:
A=1250(1.05)2 A = 1250 \left(1.05\right)^2
A=1250×1.1025 A = 1250 \times 1.1025

STEP 6

Multiply to find the final balance:
A=1250×1.1025=1378.125 A = 1250 \times 1.1025 = 1378.125
The balance after 2 years in the savings account is $1378.125\$1378.125.

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