Question

1.Find the present value at time 0 of $15086 due at the end of 4.88 years if the force of interest δ=0.023δ=0.023.

2.If an investment will double in 8.15 years at a constant force of interest δ, then

3.An investment of $1300 at t = 0 accumulates at a constant force of interest δδ= 4% for the first 4 years and at a nominal annual rate of interest of 5% compounded semiannually thereafter. Find the accumulated value of this investment at time t = 11.

4.An investment pays $1150 at time 0 and $2250 at the end of 3 years. Find the accumulated value of this investment at time 8 if the force of interest δt=0.02(1+t)2δt=0.02(1+t)2.

5.An investment of $1700 at t = 4 accumulates at a force of interest δt=0.003+0.009t2δt=0.003+0.009t2. Find the accumulated value of this investment at time t = 9.

6.How long does it take an amount to triple if the force of interest δ=0.062δ=0.062.

Answer 1

1. We know that

Therefore,

Therefore,

Thus, the present value is $13484.31

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2. Given, constant force of interest and investment doubles in 8.15 years, i.e. with . Thus, we have

Taking logarithm on both sides, we get

Thus, the force of interest required is 8.5%.

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3. Given, which is compounded annually at for . This gives the final value,

After this, it is compounded semi-annually at for years. Thus gives the final value at as

Thus, the amount at is $1813.41

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4. Given, force of interest,

Now, is the accumulation. Therefore, at

Substituting, we get

Thus, we have

Thus, we have for

Therefore,

And so, the final value at

So, the accumulated value is $189382.

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(Only 4 parts in 1 question can be solved)