Question

Suppose at your birth your parents bought you a savings certificate that had a locked-in interest rate, compounded continuously. All you know is that the value of the certificate was $1,866.79 when you were 9 years old and $3,350.87 when you were 18. How much did your parents put into the certificate at your birth?

a) $1, 020.
b) 8960.
c) $1, 040.
d) 8980.

Answer 1

Option C : P = $1040

Explanation:

Using formula for continuous compounding, we have;

FV = Pe^(rt)

Where;

FV is the future value

P is the starting principal

r is the interest rate

t is time period

Now, from the question;

After 9 years, value is 1,866.79

Hence;

Pe^(9r) = 1,866.79 - - - eq1

Also, after 18 years;

Pe^(18r) = $3,350.87

Now, from exponential functions,

e^(4) can be written as (e^(2))²

Thus,in our case, e^(18r) can simply be written as (e^(9r))²

Thus, we can write Pe^(18r) = $3,350.87 as;

P(e^(9r))² = 3,350.87 - - - eq3

Thus, dividing eq 1 by eq 3 gives;

P(e^(9r))²/Pe^(9r) = 3350.87/1866.79

e^(9r) = 1.794990331

So;

In 1.794990331 = 9r

r = 0.585/9

r = 0.065

Putting this for r in equation 1 gives;

Pe^(9 × 0.065) = 1,866.79

1.795P = 1,866.79

P = 1866.79/1.795

P = $1040