Answered: Give the present value of compound…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Give the present value of compound interest formula where PV is the present value (in dollars), FV is the future value (in dollars), r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years.

PV = ____________________

An account earns 9% interest compounded quarterly to yield $10,000 in 4 years. Determine the following values.

FV =

R =

n =

t =

How much money (in dollars) should be invested when the account is opened to produce this result? (Round your answer to the nearest cent.)

Expert Solution

Step 1

given that an account earns 9% interest compounded quarterly to yield $10,000 in 4 years. so

$\begin{array}{rcl} F V & = & $ 10, 000 \\ R & = & 9 % \\ n & = & 4 \\ t & = & 4 y e a r s \end{array}$

we have to find PV.

let PV=x, so

$\begin{array}{rcl} F V & = & P V {(1 + \frac{R}{100 n})}^{n t} \\ 10000 & = & x {(1 + \frac{9}{400})}^{16} \end{array}$

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