the washingtons are saving up to go on a family vacation in 5 years. they invest $3200 into an account with…

the washingtons are saving up to go on a family vacation in 5 years. they invest $3200 into an account with an annual interest rate of 1.45% compounded annually. 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 the washingtons account after 5 years? (b) how much interest is earned on the washingtons investment after 5 years?

the washingtons are saving up to go on a family vacation in 5 years. they invest $3200 into an account with an annual interest rate of 1.45% compounded annually. 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 the washingtons account after 5 years? (b) how much interest is earned on the washingtons investment after 5 years?

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $n$ is the number of years. Here, $P=$3200$, $r = 0.0145$ (since $1.45%=0.0145$), and $n = 5$.

Step2: Calculate the amount $A$

$A=3200\times(1 + 0.0145)^5=3200\times(1.0145)^5$. $(1.0145)^5=1.0145\times1.0145\times1.0145\times1.0145\times1.0145\approx1.07442$. $A = 3200\times1.07442=$3438.144$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. $I = 3438.144-3200=$238.144\approx$238.14$.

Answer:

(a) $$3438.14$ (b) $$238.14$