Answer 121 and 127 Show work with clear hand write please 10

10 CHAP. 1] BASIC CONCEPTS At what rate of interest, compounded annually, will an investment triple itself in (a) 8 years? (b) 10 years? 1.21 (c) 12 years? (a) 14.7%; (b) I Arts. 1.6%, (c) 96% A person lends $2000 for five years at 10% per annum simple interest, then the entire proceeds are invested for 10 years at 9% per year, compounded annually. How much money will the person have at the end of the entire 15-year period? Ans. $7102.09 1.27

Solution

1.21

answers:

(a).for 8 years

let investment be P.the amount should be 3P.

if the interest rate is r.

Amount = Principal * (1 + Rate of interest)^Years

3 * P = P*(1 + r)⁸

3P / P = (1 + r)⁸

3 = (1 + r)8

(1+ r) = (3)1/8

1 + r = 1.147

r = 1.147 - 1

r = 0.1472 = 14.72%.

(b)

for 10 years

let investment be P.the amount should be 3P.

if the interest rate is r.

Amount = Principal * (1 + Rate of interest)^Years

3 * P = P*(1 + r)10

3P / P = (1 + r)10

3 = (1 + r)10

(1+ r) = (3)^1/10

1 + r = 1.116

r = 1.116 - 1

r = 0.116 = 11.6%.

(c)

for 12 years

let investment be P.the amount should be 3P.

if the interest rate is r.

Amount = Principal * (1 + Rate of interest)^Years

3 * P = P*(1 + r)12

3P / P = (1 + r)12

3 = (1 + r)¹²

(1+ r) = (3)^1/12

1 + r = 1.096

r = 1.096 - 1

r = 0.096 = 9.6%.

so,answer for

8 years = 14.7%

10 years = 11.6%

12 years = 9.6%

question number :- 1.27

lending amount $2000

for five yeras

at 10%per annual simple interest

which means that borrower will pay back 0.1 * 2000 = $200 per year * 5years = $1000 for five years

so in five years he have to pay $3000

When lender invest it with annual compounding at 9% interest rate the total amount will be multiplied by 1.09 years.

A = P(1 + r)^t

where A is money after investing

P is the initial amount invested

r is the interest rate = 9% = 0.09

and t is the number of years

Therefore,

A = 3000( 1 + 0.09)¹⁰

A = 3000(1.09)¹⁰

= 3000 * 2.36736

= $7102.09102

so the person will have 7102.09 at the end of the entire 15 year period.

in simple it can be written as:

2000 * (1 + 0.1)⁵ = 3000 after five years

then 3000(1.09)¹⁰ = $7102.09