Question

1. A young lady invested $50 to plant Christmas trees on her grandfather's farm. When the lady was a first year student in college, six years later, she harvested the trees and sold them for $490. What annual rate of return (i.e. interest rate) did she earn on the investment, assuming she incurred no expenses in the interval?

2. Find the future value in 2 years of $99 that is deposited in an account which pays 12% annual rate with monthly compounding.

3. A 30 year mortgage bears annual interest at 12% and has a principal of $145,852. What will the monthly payments equal assuming monthly compounding?

Answer 1

Question 1:

Amount invested = $50

Sale Value = $490

n = 6 years

r = annual interest rate

(1+r)^n = Sale Value / Amount invested

(1+r)^6 = $490 / $50

(1+r)^6 = 9.8

1+r = 1.46286533

r = 0.46286533

r = 46.29%

Therefore, annual interest rate is 46.29%

Question 2:

Present Value = PV = $99

r = Monthly interest rate = 12%/12 = 1%

n = 2*12 = 24 months

Future Value = PV * (1+r)^n

= $99 * (1+1%)^24

= $99 * 1.26973465

= $125.70373

Therefore, future value in 2 years is $125.70

Question 3:

PV = Principal Amount = $145,852

n = 30 *12 = 360 months

r = monthly interest rate = 12%/12 = 1%

Monthly Payment = [r*PV] / [1 - (1+r)^-n]

= [1%*145,852] / [1 - (1+1%)^-360]

= $1,458.52 / 0.972183311

= $1,500.25205

Therefore, monthly payment is $1,500.25