Question

1. Interest Periods and Compounding

a) Your family loans you money for school at a simple interest rate of 5%. If the original amount they provided was $20,000 what will you be paying them back in 5 years?

b) You have 10 acres of land that can be used for residential development. It is worth $20,000 per acre right now. What would it be worth in 6 years if it appreciates at a rate of 6% compounded annually?

c) Which will happen sooner under a 6% annual compounding interest rate? $20,000 becomes 30,000 or$180,000 becomes $215,000?

d) At a compounding interest rate of 2.5% per month, money will triple in value in how many months?

e) $20,000 today is equivalent to $47,000 in 20 years. What is the annual simple interest rate?

Answer 1

Given data simple interest rate (r) = 5 % original amount (p) = 20000 time (t) = 5 years simple interest (s.i) = ptr/100 s.i = 20000 times 5 times 5/100 s.i = 5000 total amount you be paying them back is 5 years = original amount + s.i 20000 + 5000 total amount = 25000given data amount principal (p) =$ 20000 time (t) = 6 years rate (r) 6% total amount after 6 years (compound annually a = p[(1 + r/100)^n] a = 20000 [(1 + 6/100)^6] a = $28370.38 \r\n compound interest (ci) = p[(1 + r/100)^n-1] c.i = 2000[(1 + 6/100)^6-1] c i = $8370.38 given data annual compounding interest rate = 6% 20000 become 30000 principle amount 20000 final amount = 30000 time n = ? a = p[(1 + r/100)^n] 30000 = 20000[(1 + 6/100)^n] n = 6.95 approximately n = 7 years 180000 becomes 215000 principle amount = 180000 final amount = 215000 time n = ? a = p[1 + r/100]^n \r\n 215000 = 180000[1+(6/100)^n] n = 3.049