to help with her retirement savings, kala has decided to invest. assuming an interest rate of 3.51%…

to help with her retirement savings, kala has decided to invest. assuming an interest rate of 3.51% compounded quarterly, how much would she have to invest to have $132,700 after 18 years? do not round any intermediate computations, and round your final answer to the nearest dollar. if necessary, refer to the list of financial formulas.

to help with her retirement savings, kala has decided to invest. assuming an interest rate of 3.51% compounded quarterly, how much would she have to invest to have $132,700 after 18 years? do not round any intermediate computations, and round your final answer to the nearest dollar. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Identificar la fórmula de valor presente

La fórmula para el valor presente $P$ con interés compuesto es $P = \frac{A}{(1+\frac{r}{n})^{nt}}$, donde $A$ es el valor futuro, $r$ es la tasa de interés anual (en decimal), $n$ es el número de veces que se compone el interés por año y $t$ es el número de años.

Step2: Convertir la tasa de interés a decimal

$r = 3.51%=0.0351$.

Step3: Identificar $n$ y $t$

Como el interés se compone trimestralmente, $n = 4$, y $t = 18$ años. $A=132700$.

Step4: Calcular $(1+\frac{r}{n})^{nt}$

Sustituir los valores: $(1+\frac{0.0351}{4})^{4\times18}=(1 + 0.008775)^{72}$. Usando una calculadora, $(1 + 0.008775)^{72}\approx1.8777$.

Step5: Calcular el valor presente $P$

$P=\frac{132700}{(1 + 0.008775)^{72}}=\frac{132700}{1.8777}\approx70671$.

Answer:

$70671$