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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 22 (page 351)

(a) If \(1000 is invested at 5% compounded monthly, how much is there after 8 months?
(b) If you want to have \)1000 in 9 months, how much do you need to place in a savings account now that pays 5% compounded quarterly?
(c) How long does it take to double your money if you can invest it at 6% compounded annually?

Short Answer

Expert verified

(a) After 8 months, $1000 investment is worth $1033.8.

(b) We need to invest $963.42 to $1000 after 9 months.

(c) If the interest is compounded annually, it takes 11.9 years for the investment to double.

Step by step solution

01

Step 1. Given Information

Given that

$P = $ 1000 r = 5 % = 0.05 n = 12 t = \frac{8}{12} = \frac{2}{3} y e a r$

02

Part (a) Step 1. Finding amount after 8 months

Fro compound interest formula

A = P {(1 + \frac{r}{n})}^{n t} A = 1000 {(1 + \frac{0.05}{12})}^{12 路 \frac{2}{3}} A = $ 1033.82

03

Part (b) Step 1. Finding Principal

Notice how do we need to calculate present value P, if the compound interest formula is $A = P {(1 + \frac{r}{n})}^{n t}$ then $P = A {(1 + \frac{r}{n})}^{- n t}$

$P = 1000 {(1 + \frac{0.05}{4})}^{- 4 路 \frac{3}{4}} P = $ 963.42$

04

Part (c) Step 1. Finding time to double money

Using the compound interest formula

$A = P {(1 + \frac{r}{n})}^{n t} 2 P = P {(1 + \frac{r}{n})}^{n t} 2 = {(1 + \frac{0.06}{1})}^{1 t} 2 = 1 . 06^{t} \ln (2) = t \ln (1.06) t = \frac{\ln (2)}{t \ln (1.06)} = 11.9 y e a r s$

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