Compound Interest?

Question

You invest $4075 at 6.3% per annum compounded quarterly. Determine the number of quarters required for your investment to exceed $13150. Round any partial quarter up to the next quarter.

Answer 1

The unknown is n, the number of quarters it takes for your investment to equal $13,150.

$4,075 * (1+6.3%/4)^n = $13,150

Divide both sides by $4,075

(1+6.3%/4)^n = $13,150/$4,075

Take logarithms of both sides

n*ln(1+6.3%/4) = ln(13,150) - ln(4075)

n = [ln(13,150) - ln(4075)]/ln(1+6.3%/4)

Since 6.3% = 0.063

n = [ln(13,150) - ln(4075)]/ln(1+0.063/4)

n = [ln(13,150) - ln(4075)]/ln(1.01575)

Now just plug this into your calculator

n = (9.484177 - 8.312626)/0.015627

n = 74.968441

Since the question is how long it takes for your investment to exceed the amount, we need to round up so

n=75 quarters

Answer 2

Evaluate the formula 4075*(1 + .063/4)^(4*t). You should find with t = 18, the value is 12553; with t = 19, the value is 13363.

Answer 3

4075(1+0.063/4)^n = 13150
1.01575^n = 3.227
n = ln(3.227)/ln(1.01575)
n = 74.96
n ~ 75 quarters

Answer 4

75 quarters.

Answer 5

See if you can find youself by using this site calculator
http://www.moneychimp.com/calculator/compound_interest_calculator.htm