Question

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Problem #9 : A deposit of $6,0 0 earns a continuous force of interest given by 0041 for the first 5 years (t s time in years), and a constant force of 0.2 thereafter. What nominal quarterly compounding rate is earned over the first 7 years? Answer as a percentage correct to 2 decimals. Problem #9: | Just Save Your work has been saved! (Back to Admin Page) Submit Problem #9 for Grading Problem #9| Attempt #1 Your Answer: Attempt #2 | Attempt #3 Attempt #4 Attempt #5 Your Mark:

Answer 1

The answer is 1.69 %( rounded to 2decimals)

Calculation

From the above question we can clearly interpret that there is no yearly compounding and it is simple interest

For simple caluculation purpose we will take principle amount is 100 (answer does not change with principle amount )

Interest for hundred rupees =100×0.04×5+100×0.2×2=60

So amount plus principle is 160

Let quarterly compounding rate is x

Caluculation of amount formulae

A=p(1+x)^nt

A= future value of amount

P= principle

N= no of times compounded per year

So 160=100(1+x)^4×7

8/5=(1+x)^28

1+x=1.6^1/28

By using caluculation x=0.0169

So effective compound interest rate is 1.69%

Cross check

In simple interest way 6000×0.04×5+6000×0.2×2=3600

Compounding interest

=6000×(1.069)^28= 3600