Question

13.) You invest $5500 in a bond that pays an annual compound interest rate of 6.75%. How many years will it take for this bond to be worth triple (3 times the initial value)? Show your equation, substitution, all algebra work, and correct answer? Show work

Answer 1

The investment value of Bond is $5500.

The bond pays a compounding interest rate of 6.75%.

We need to find out the number of years by which the initial value of the bond triples i.e it becomes = $5500*3= $ 16,500.

Lets take the number of years within which the bond value triples be 'n' years.

So, the formula for compounding is;

(Principal * (1 + interest rate)^n = Future Value;

so; ( $5500 * (1 + (6.75/100))^n)= $ 16,500

or; ( $ 5500 * (1+ 0.0675)^n)= $ 16,500

or; ($5500 * (1.0675)^n)= $ 16,500

By putting $5500 on the right side ;

or; (1.0675 ^ n)= ($16,500/ $ 5,500)

or; (1.0675^ n)= 3

Now; putting Log ( logarithm on both sides);

We have ;

or; Log (1.0675)^n= Log 3

or; n log (1.0675) = log 3;

We know; Log 1.0675= 0.02837 and Log 3= 0.477121

Therefore;

or; n = (log 3/log 1.0675)

or; n = (0.477121/ 0.02837)

or; n = 16.94

This means, the initial value gets tripled to $ 16,500 in 16.94 years or 17 years ( approx).

16.94 years= 16 years 11 months or 17 years.

Ans: The initial value of the bond gets tripled in 17 years (approx) or 16.94 years.