Question

How long will it take a sum of money to double if interest is at 11% compounded semiannually?

Answer #1

Rate = 11% (semi-annual compounding),

Converting Rate into effective rate = r = (1+R/2)^2-1 = (1+11%/2)^2-1 = 11.3025%

Assuming invested amount = PV = $ 100

Expected amount is double of invested amount = FV = $ 200

Time = Tenor in years = t = ?

Formula of Present Value or PV:

PV = FV / (1+r)^t

100 = 200/(1+11.3025%)^t

100 = 200 / (1.113025)^t

(1.113025)^t = 200/100

(1.113025)^t = 2

Take natural log at both the sides;

t x ln(1.113025) = ln(2)

t x 0.107081534 = 0.693147181 **[See note
below]**

t = 0.693147181 / 0.107081534

t = 6.473078556

**t = ~ 6.47 years**

**Note:** Value for ln(1.113025) = 0.107081534 and
ln(2) = 0.693147181

How long will it take to double your money at 6% interest
compounded annually?

6. How long does it take to double your money at 10 percent
interest? How long does it take to quadruple your money?
Input area:
Output area:
Present value
Years
Interest rate
Future value
$
1.00
***?
10%
$
2.00
1.00
***?
10%
4.00

How long would it take a sum to double if the growth rate was 5%
per year?
How long would it take a sum to triple if the growth rate was 5%
per year?

At 5 percent interest, how long does it take to double your
money? (Do not round intermediate calculations and round
your answer to 2 decimal places, e.g., 32.16.)
Length of time
years
At 5 percent interest, how long does it take to quadruple your
money? (Do not round intermediate calculations and round
your answer to 2 decimal places, e.g., 32.16.)
Length of time
years

At 6.5% interest, how long does it take to double your
money?
(Do not round intermediate calculations. Round your answer to 2
decimal places.)
Length of time years At 6.5% interest, how long does it take to
quadruple it?
(Do not round intermediate calculations. Round your answer to 2
decimal places.) Length of time years

5-13 TIME FOR A LUMP SUM TO DOUBLE How long
will it take $300 to double if it earns the following rates?
Compounding occurs once a year.
a. 6%
b. 13%
c. 21%
d. 100%

At 6.1 percent interest, how long does it take to double your
money? (Do not round intermediate calculations and round your
answer to 2 decimal places, e.g., 32.16.) Length of time years At
6.1 percent interest, how long does it take to quadruple it? (Do
not round intermediate calculations and round your answer to 2
decimal places, e.g., 32.16.) Length of time years.

How long will it take for $1,000 to double if the interest rate
is 4%? If the interest rate is 8%? If the
interest rate is 12%?

How long would it take to triple your money if the interest rate
was:
5% compounded yearly
5% compounded monthly
5% compounded weekly
5% compounded continuously

We sometimes need to find how long it will take a sum of money
to grow to some specified amount. For example, if a
company’s sales are growing at a rate of 20% per year,
approximately how long will it take sales to triple?

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