Respuesta :
Answer:
They should deposit $45,467.95 now.
[tex]\text{ \$}45,467.95[/tex]Explanation:
The formula for calculating the future value of compound interest can be written as;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where;
A = Future amount
P = Principal (initial amount)
r = Interest rate (decimal)
n = number of times the interest is compounded per unit time "t"
t = time
Making the Principal (P) the subject of formula in the formula above we have;
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Given;
A = Future amount = $160,000
r = Interest rate (decimal) = 7% = 0.07
n = number of times the interest is compounded per unit time "t" = 2(12) = 24 times per year
(Twice in a month times 12 months in a year.)
t = 18 years
substituting the given values into the formula above, we have;
[tex]\begin{gathered} P=\frac{160,000}{(1+\frac{0.07}{24})^{24(18)}}=\frac{160,000}{(1+\frac{0.07}{24})^{432}} \\ P=\text{ \$}45,467.95 \end{gathered}[/tex]Therefore, They should deposit $45,467.95 now.
[tex]\text{ \$}45,467.95[/tex]