logarthmic equation questions

Question

1.How long, to the nearest tenth of a year, will it take a $5000 investment to double if the money is invested at 7% interest compounded quarterly? How long will it take to triple the investment?

 

 

2. .use the formula pv=r-(1+i)^-n/i for the question below

• PV  present value
• i  interest rate per compounding period, as a decimal
• R  payment amount
• n number of payments

 Suppose a bank offers you a 3.4% interest rate, compounded semi-annually, on a mortgage amount of $173 112. You pay $1000/mo, or $6000 semi-annually. How many semi-annual payments would you have to make to pay off the mortgage? How long, in years, would it take to pay off the mortgage?

 

Answer 1

1.  For any investment to become k times the initial investment, we can say

kP = P(1+r/n)^nt where compounding of r % occurs n times per year, for t years.

This equation can be divided by P, the original Principal, on both sides.

Then ln k = nt ln(1+r/n). Solving for t gives

t = (ln k)/[n ln (1+r/n)]

 

In your case, k = 2 for doubling, n = 4 (quarterly), r = 0.07, and time to double is 9.99 years.

Use k = 3 to find tripling time.