Thursday, August 23, 2018

College Algebra, Chapter 5, 5.4, Section 5.4, Problem 74

Suppose that a woman wants to invest $4000 in an account that pays 9.75% per year, compounded semiannually. How long a time period should she choose to save an amount of $5000?



Recall that the formula for interest compounded n times per year is..

A(t)=P(1+rn)nt

So if the interest is compounded semiannually, then n=2


5000=4000(1+0.09752)(2)t50004000=(1+0.09752)2tln(54)=ln(1+0.09752)2tln(54)=2tln(1+0.09752)ln(54)2ln(1+0.09752)=tt=2.34 yearst=2 years+0.34 years(12 months1 year)t=2 years+4.08 months


It shows that the woman will save an amount of $5000 if the period is approximately 2 years and 5 months.

No comments:

Post a Comment

Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...