I have a word problem that I think involves logs. I really need help and I am so confused.

Question

Katherine's grandparents deposit $5000 in her college fund in honor of her birth. The money is in a bond fund at 7% interest compounded annually. How much money is in the account after 18 years have gone by?

 

I am not sure how to start this. I really do appreciate all of the help.

Thanks

Answer 1

FV = PV * (1+ r)ⁿ

 

FV (Future Value)

PV (Present Value of $5000)

r (Intrest rate of 7%)

n (number of periods 18 years)

 

FV = 5000 * (1+0.07)¹⁸

 

The answer is FV = $16,899.66

 

Note: the above formula can be used only in the event of annual compounding.

 

 

 

 

Answer 2

We will use the formula

 

A = P(1 + (r/n))^nt

 

where:

A = amount accumulated

P = investment

r = interest rate

t = time

n = number of time compounded per year

 

Given:

P = 5000

r = 0.07

n = 1

t = 18

 

We use logs when finding the value of the exponent.  For example:

 

10^x = 152

 

Solve for x.

 

1)    log10^x = log(152)          Log both sides of equation

 

2)   xlog10 = log(152)          Bring the exponent as the coefficient of log

 

3)   x = log(152) / log(10)    

 

Since your exponents n and t is known, using logs will not be necessary.  We just substitute these values into the formula.

Answer 3

A = p(1 + r/n)^nt, where p = principal, r = rate, n = number of calculations per year, t = time in years

 

A = 5000(1 + 0.07)¹⁸

A = 5000(1.07)¹⁸

A = 5000(3.37993228)

A = 16899.66