Question

In: Finance

Ahmad is looking for an investment tool that will double his money in five years. a)...

Ahmad is looking for an investment tool that will double his money in five years.

a) What interest rate (compounded annually), to the nearest whole percentage, does he have to receive?

b) At that rate, how long will it take the money to triple?

ANS
a) 15% b) 7.86 years OR 7 years 10 months

Pls attach the formula used, and explain in detail. Pls do not answer in excel format. Thank you in advance.

Solutions

Expert Solution

The formula used to calculate compound interest is given by:

Final amount=Principal amount*(1+rate of interest)^Time period

Part a:
Final amount is double of the principal amount
So, if principal is denoted as "P", final amount=2P
Suppose rate of interest is denoted as "r", time period is given as 5 years. Substituting the values in the equation, we get:
=>2P=P*(1+r/100)^5
=>2=(1+r/100)^5
=>3^1/5=1+r/100
=>1.148698355=1+r/100
=>1.148698355-1=r/100
=>0.148698355=r/100
0.148698355*100=r
So, rate of interest=14.8698% or 15% (Rounded to nearest whole percentage as given in the question)

Part b:
At the rate of 15%, the time period it will take for the amount to triple is:
If principal is denoted as "P", final amount=3P

3P=P(1+15%)^n
3=(1+.15)^n
=>3=(1.15)^n
=>3=1.15^n
Now, taking log function in both the sides, we get
ln3=ln(1.15^n)
=>ln3=n*(ln1.15)
1.098612289=n*0.139761942

n=1.098612289/0.139761942=7.860596907 or 7.86 years or 7 years + (12 months*.86=10.32 months) that will result in 7 years and 10 months

Note: The values of ln(3), ln(1.15) or any ln or log value can be calculated using calculator or excel or logarithmic tables.


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