Find the missing values assuming continuously compounded interest.

Question

Initial Investment = 650

Annual % Rate = ?

Time to double = 6,1/5 yr

Amount after 10 years = ?

Answer 1

Hi Xavier B.,

For continuously compounded interest we use the equation A = A_oe^rt, where A_o is the initial investment, r is the interest rate, t is the time (yrs.) invested, and A is the amount after time t.

We can use the initial investment of $650 and a doubling time (A = $650*2 = $1300) of 31/5 years to find the rate r:

1300 = 650e^r(31/5)

2 = e^r(31/5)

ln(2) = ln(e^r(31/5))

ln(2) = r(31/5)

r = ln(2)/(31/5) = 5*ln(2)/31 = ln(32)/31

We can now find the amount at a time of 10 years:

A = 650e^10*ln(32)/31 = 1988.13

I hope this helps, Joe.

Answer 2

the underlying formula that you want to use here for continuous compounding is

A = P*e^(rt)

for doubling time you can take

t(double) = ln(2) / r

r = ln(2) / t(double)

r = ln(2) / 6.2 = 0.1118

so putting it all together this scenario means taking

A = 650 * e^(0.1118*10)

A = 1988.13

meaning that the accumulated amount in the account after 10 years is $1,988.13