Answer to Question #120234 in Financial Math for Danelle Sammy

Question

1)A sum of $9, 000 paid into a bank account for two months (61 days) to attract simple interest will produce $9, 020 at the end of the term. Find the interest rate r and the return on this investment.
2)How much would you pay today to receive $1, 000 at a certain future date if you require a return of 2%?
3)How long will it take for a sum of $800 attracting simple interest to become $830 if the rate is 9%? Compute the return on this investment.
4)Find the principal to be deposited initially in an account attracting simple interest at a rate of 8% if $1, 000 is needed after three months (91 days).
5)How long will it take to double a capital attracting interest at 6% compounded daily?
6)What is the interest rate if a deposit subject to annual compounding is doubled after 10 years?

Answer 1

Question 1)

A = P(1+rt)

9,020 = 9,000 (1+r(2/12)

 1+r(0.166667) = 1.002222

0.166667r = 0.002222

r = 0.002222/0.166667

r = 0.013331973 ~ 1.33%

Return on investment (ROI) = (9,020 – 9,000)/9,000

Return on investment (ROI)  = (20/9,000)*100% ~ 0.22%

Question 2)

PV = FV/(1+r)

PV =1,000 /(1+0.02)

PV=1,000 / 1.02

PV = 980.392157

Question 3)

A = P(1+rt)

830 = 800 (1+0.09*t)

 (1+0.09*t) = 830 / 800

1+0.09*t = 1.0375

0.09*t = 0.0375

t = 0.0375/0.09

t = 0.41666667 ~ 5 months

Return on investment (ROI) = (830 – 800)/800

Return on investment (ROI)  = (30/800)*100% ~ 3.75%

Question 4)

P = A / (1+rt)

P = 1,000 / (1+0.08*3/12)

P = 1,000 / (1+0.020)

P = 1,000 / 1.020

P = 980.392157

Question 5)

A = P * (1+rt)

A = 2*P = 2P

2P = P(1+ (6/365)*t)

1+ (6/365)*t = 2P/P

0.016438t = 2 – 1

t = 1 / 0.016438

t = 60.83465142

t = 60.83465142 days

Question 6)

Principal = P

Amount = 2*P = 2P

2P = P*r¹⁰

R¹⁰ = 2P/P

R¹⁰ = 2

10log R = log2

Log R = log 2 / 10

Log R = 0.693147 / 10

Log R = 0.0693147

r = ln^-10.0693147

r = 1.173%