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Start decomposing this problem. Level Annuity Case Consider some level annual payments of $1$ over $20$ years at interest rate $i$. For each payment $X_t = 1$ for $t = 1, 2, \dots, 20$, we define $I_t$ to be the interest portion of $X_t$ and $P_t$ to be the principal portion of $X_t$ ($\boxed{X_t = I_t + P_t}$). Let $B_t$ be the balance of the annuity at ...


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In general you have to know how Exel or a online calculator work. Do they consider outflows/inflows at the end of the first year as outflows/inflows in the first year or in the second year ? In general the NVP is the value of the sum of all discounted outflows/inflows at the $\texttt{beginning}$ of the first year. Your table Looks right. The NVP of your ...


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Note that $\delta$ is constant if and only if $i$ is constant, and if $i$ is constant, we define $v = \dfrac{1}{1+i}$. So actually, the formula $$a_{\overline{n}|} = \sum\limits_{j=1}^{n}v^j\tag{1}$$ is only true for constant $i$, and therefore constant $\delta$. One problem I've had with actuarial texts is that they seem to be ambiguous with their ...


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The accumulated value of a cash flow under compound interest can be calculated by regarding each individual payment separately, then taking the sum of their accumulated values at the same time point. In your case, the first payment of $3600$ has had $11$ years to compound interest at an $i = 0.10$ annual effective rate, thus its accumulated value at the end ...


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Take a zero coupon bond due in $t$ years, when it will pay $100$. If the present interest rate is $r$ per year, it is now worth $\frac {100}{(1+r)^t}$ If interest rates change to $s$ per year, it will then be worth $\frac {100}{(1+s)^t}$. The new value is $\frac {(1+r)^t}{(1+s)^t}$ of the old one. As long as $rt, st \ll 1$ we can keep only the first ...



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