Question

THE QUESTION IS THAT I NEED A NARRATIVE ANALYSIS.............ON PROBLEM 3.

I HAVE THE ANSWER I NEED THE NARRATIVE ANALYSIS AND WHAT WOULD YOU RECOMMEND TO THE COMPANY.

PLEASE DO NOT WRITE OUT THE ANSWER THAT I ALREADY HAVE.

How many years will it take for $197 million to grow to be $554 million if it is invested in an account with a quoted annual interest rate of 5 percent with monthly compounding of interest?

Question 1 Monev at the end of cumulatig vears (FV)-PV x (1trAN PV 95 Million FV = Future Value PV = Present Value r = Interest Rate (as a decimal value), and n Number of Periods 3.5 10 FVI 95* ( 1+.035) Λ10 134.01 Milllion Question 2 Money need to invest to get 14 Million after 13 vears PV FV/ (1+r)An 1+.04 13-$ 1.67 Money need to invest to get 14 Million after 13 years 14 Million /1.665073 8.41 Million Question 3 Cumulative interest Factor to Grow to 554 Number of Years ( n )In = In(FV / PV) / ln(1 + r) Monthly interest rate .05/12-.004166667 Number of Months= | In554/197)/In(1+.004166 Number of Months Number of Years (n) 248.67 20.7225

Answer 1

As you are already aware of the answer. Let me break it for you step by step.

Step 1 : Calculation of Effective Annual Rate(EAR)

Since it is given that the money grows at a stated interest rate of 5% p.a with monthly compounding so we need to calculate the EAR p.a with annual compounding to match the compounding rate and the number of periods that we need to calculate (i.e. no. of year in this case)

$EAR = (1+\frac{R{s}}{m})^m -1$

m = frequency of compounding i.e. 12 in the case of monthly

r_s = stated annual rate i.e. 5%

By plugging in the values we calculate EAR = 5.11618% compounded annually

Step 2 : Calculation of number of years

Recall from Time Value of Money. The simple expression to calculate the Growth in money over time is given by the following formula:

$FV = PV * (1+EAR)^n$

Here, Future Value = $554

Present Value = $197

EAR = 5.11618%

554 = 197 * (1+5.11618%)^n

Take log_e on both sides

ln 554 = ln (197 * (1+0.0511618)^n)

ln 554 =ln 197 + n* ln 1.0511618

Using the calculator, we find n= 20.722 years

Therefore, Company need to invest $197 million for 20.72 years at effective annual rate of 5.11618% p.a. compounding annually (or 5% p.a. compounding monthly) to reach $554 million