punyadeep wrote:
Q A certain sum was invested in a high-interest bond for which the interest is compounded monthly. The bond
was sold x number of months later, where x is an integer. If the value of the original investment doubled
during this period, what was the approximate amount of the original investment in dollars?
(1) The interest rate during the period of investment was greater than 39 percent but less than 45 percent.
(2) If the period of investment had been one month longer, the final sale value of the bond would have
been approximately $2,744.
Investment = $P
time: x months = x/12 years
Periods = n = 12
Return after application of the compound Interest for x months;
\(P(1+\frac{r}{n})^{nt}\)
\(P(1+\frac{r}{12})^{12*x/12}\)
\(P(1+\frac{r}{12})^x\)
It is given that the investment doubles after x months;
\(P(1+\frac{r}{12})^x=2P\)
\((1+\frac{r}{12})^x=2\)
r and x are unknown
1. 0.4<=r<=0.44
\((1+\frac{0.4}{12})^x=(1.033)^x = 2\)
to
\((1+\frac{0.44}{12})^x=(1.036)^x=2\)
x can be found; but we don't know P.
Not Sufficient.
2.
\(P(1+\frac{r}{12})^{(x+1)}=2744\)
\(P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744\)
\(2P*(1+\frac{r}{12})=2744\)
We still have two unknowns.
Not Sufficient.
Combining both;
r= 0.4
\(2P*(1+\frac{0.4}{12})=2744\)
Now, we can get approx value of P.
Ans: "C"