Question

In the following problems, find (a) the compound amount and (b) the compound interest for the given investment and annual rate. 1. $4,000 for 7 years at 6% compounded annually. 2. $5,000 for 20 years at 5% compounded annually. 3. $700 for 15 years at 7% compounded semiannually. 4. $3,000 for 16 years at 8¾% compounded annually. 5. $2,000 for 12 years at 9% compounded quarterly. 6. $8,000 for 3 years at 6¼% compounded daily. (Assume that there are 365 days in a year.)

Answer 1

To find the value of the compound amount and compound interest:

where A rep Amount

I rep compound interest

(1.a) $4,000 for 7 years at 6% compounded annually.

First, convert R as a percent to r as a decimal

r = R/100

r = 6/100

r = 0.06 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 4,000.00(1 + 0.06/1)(1)(7)

A = 4,000.00(1 + 0.06)(7)

A = $6,014.52

(b) I = A - P

`\begin{gathered} I\text{ = \$ 6014.52}-4000 \\ I=\text{ \$2014.52} \end{gathered}`

(2a) $5,000 for 20 years at 5% compounded annually.

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.05/1)(1)(20)

A = 5,000.00(1 + 0.05)(20)

A = $13,266.49

(b) I = A -P

`\begin{gathered} I=13266.49-8000 \\ =5266.49 \end{gathered}`

(6a) $8,000 for 3 years at 6¼% compounded daily.

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,000.00(1 + 0.03/365)(365)(20)

A = 8,000.00(1 + 8.2192E-5)(7300)

A = $14,576.61

(b) I = A - P

`\begin{gathered} I=\text{ \$14576.61-8000} \\ I=\text{ \$6576.61} \end{gathered}`