At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
We have to find the present value that can make quarterly payments of $4000 for 7 years, with an nominal interest rate of 6% compounded quarterly.
As it is compounded quarterly, we have 3 subperiods in a year. Then, the parameter m, the number of subperiods, is m=3.
The number of yearly periods is n=7.
The interest rate is r=0.06.
The payment is P=4000.
We have to use the annuity formula to calculate the present value:
[tex]\begin{gathered} PV=P\cdot\frac{1-\frac{1}{(1+\frac{r}{m})^{n\cdot m}}}{\frac{r}{m}} \\ PV=4000\cdot\frac{1-\frac{1}{(1+\frac{0.06}{3})^{7\cdot3}}}{\frac{0.06}{3}} \\ PV=4000\cdot\frac{1-\frac{1}{(1+0.02)^{21}}}{0.02} \\ PV\approx4000\cdot\frac{1-\frac{1}{1.5157}}{0.02} \\ PV\approx4000\cdot\frac{1-0.66}{0.02} \\ PV\approx4000\cdot\frac{0.34}{0.02} \\ PV\approx4000\cdot17 \\ PV\approx68000 \end{gathered}[/tex]Answer: the lump sum is approximately $68,000.
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
