4) rosa invests her tax return check into an account with a compounded interest rate of 1 3/4 %. she plans…
4) rosa invests her tax return check into an account with a compounded interest rate of 1 3/4 %. she plans on keeping the account open for 12 years. if she has $1600.87 in her account at the end of 12 years, approximately how much was her initial investment? $7,690 $1,300 $1,970 $11,000
Answer
Explanation:
Step1: Identify compound - interest formula
The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal (initial investment), $r$ is the annual interest rate as a decimal, and $t$ is the number of years. First, convert the interest rate $r = 1\frac{3}{4}%=\frac{7}{4}% = 0.0175$ and $A=$1600.87$, $t = 12$ years. We need to solve for $P$.
Step2: Rearrange the formula for $P$
From $A = P(1 + r)^t$, we can get $P=\frac{A}{(1 + r)^t}$.
Step3: Substitute values into the formula
$P=\frac{1600.87}{(1 + 0.0175)^{12}}$. Calculate $(1 + 0.0175)^{12}$. Using the formula $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$, or simply using a calculator, $(1.0175)^{12}\approx1.231$. Then $P=\frac{1600.87}{1.231}\approx1300$.
Answer:
B. $1,300$