Question

The formula for the future value V (in dollars) of an investment earning simple interest is V=p+prt, where p (in dollars) is the principal, r is the annual interest rate (in decimal form) and t is the time (in years).
a. Solve the formula for p.

An investment earns 6% simple interest. What amount of principal is needed to have $3000 after 5 years? Round your answer to the nearest cent.

Amount of principal: $

Answer 1

Answer:

A. $p=\dfrac{V}{1+rt}$

B. $2,307.69

Step-by-step explanation:

You are given the formula

$V=p+prt,$

where V = investment earning simple interest

p = principal,

r = interest rate

t = time

So,

A. $V=p(1+rt)\\ \\p=\dfrac{V}{1+rt}$

B. r = 0.06 (or 6% as percent)

V = $3,000

t =5

so,

$3,000=p+p\cdot 0.06\cdot 5\\ \\3,000=p+0.3p\\ \\1.3p=3,000\\ \\p=\dfrac{3,000}{1.3}\approx 2,307.69$