Suppose $7,500 is compounded monthly for 30 years. If no other deposits are made, what rate is needed for the balance to double in that time?

Answer 1

7500(1 + x/12)^12(30) = 15000

x = 0.0232127 or 2.32127% interest rate

Answer 2

Hi Hadassah, let's address your question.

The compound interest formula is A = P(1+i)^n where A = final amount, P = initial principal, i = monthly percentage rate of interest, and n = number of periods (i.e., months) involved.

Let the required rate be i% per year. Since interest is compounded monthly, each month adds i/12 interest.

The principal is doubled, so: A = 2P.

And the number of periods is 12 x 30 = 360, the number of months in 30 years.

Hence, we have 2P = P(1+ i/12)^360

2 = (1+ i/12)^360 [dividing through by P]

This is an exponential equation, so we need to take logs on both sides. We can use log to base 10 or natural log, to base e - the answer will be the same.

Taking logs log 2 = 360 log (1 + 1/12) [by the rules for logs; exponents become multiplication]

Reorganizing: log (1 + i/12) = log2 / 360 = 0.00083619

So: (1 + i/12) = antilog (0.00083619) = 1.0008365

i/12 = 0.0008365 [subtracting 1 from both sides]

Therefore: i = 12 x 0.0008365 = 0.0100384

And we have = 1.00% per year, to 2 decimal accuracy

As a check, we would expect a low interest rate (like 1% py) since this investment takes 30 years to double.

Answer 3

2 = p(1 + r/12)^(30)(12)

Can you calculate p and answer?