MATH SOLVE

2 months ago

Q:
# Find the time required for an investment of $5000 to grow to $8000 at an interest rate of 7.5% per year, compounded quarterly.

Accepted Solution

A:

Answer: 6.3 yearsStep-by-step explanation:To find the time in years, we will use the Compound interest formula: F = P( 1 + i/m)^mnWhere F = future value of investment ($8000); P = Amount invested ($5000); Ii = interest rate (7.5%); m = number of times money is compounded in a year (m = 4 for quarterly) and n = time of investment in yearsSubstituting; 8000 = 5000( 1 + 0.075/4)^4n Divide both side by 5000 and simplify the bracket on the right hand side; 8000/5000 = (1.01875)^4n 1.6 = (1.01875)^4nSince n is the power, to solve for it we can introduce the natural logarithm ( ln); ln (1.6) = ln (1.01875)^4nThe power can betaken down according to the Laws of logarithms; ln (1.6) = 4n x ln(1.01875)To get n, divide both sides by 4ln (1.01875); ln (1.6)/ 4ln(1.01875) = n Therefore; n = 6.3 years