Determine the principal that must be invested at rate r,compounded monthly,so that $\$ 900,000$ will be available for retirement in t years. $r = 3 \frac { 1 } { 2 } \% , t = 15$
A) $\$ 532,806.81$
B) $\$ 632,806.81$
C) $\$ 432,806.81$
D) $\$ 732,806.81$
E) $\$ 332,806.81$

Question

Determine the principal that must be invested at rate r,compounded monthly,so that $\$ 900,000$ will be available for retirement in t years.​ $r = 3 \frac { 1 } { 2 } \% , t = 15$ ​
A) $\$ 532,806.81$
B) $\$ 632,806.81$
C) $\$ 432,806.81$
D) $\$ 732,806.81$
E) $\$ 332,806.81$

Quizplus · Accepted Answer

The principal can be found using the formula for compound interest: $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$, where $P$ is the principal, $A$ is the amount (future value), $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time in years. Substituting $A = \$900,000$, $r = 0.035$, $n = 12$ (since it's compounded monthly), and $t = 15$, we can solve for $P$.

Determine the Principal That Must Be Invested at Rate R,compounded $900,000\$ 900,000$900,000

Determine the Principal That Must Be Invested at Rate R,compounded $\$ 900,000$