How to solve Annuities — solving for the payment or the term of a level annuity questions on Exam FM?

Question

A level annuity-immediate has present value $\text{PV} = 46763.07$ and runs for $n = 13$ periods at an effective rate per period of $i = 4.4\%$. Calculate the level payment $P$.

Accepted Answer

Formula
With $v=(1+i)^{-1}$, $a_{\overline n|}=(1-v^n)/i$, $\ddot a_{\overline n|}=(1+i)a_{\overline n|}$, and $PV=P\,a_{\overline n|}$ (or $P\,\ddot a_{\overline n|}$).

Why this formula applies
Write the annuity present-value equation at the valuation date with payment timing matched to immediate or due. Isolate the requested payment count, payment amount, or rate only after the cash-flow equation is correct.

Substitution and calculation
With $i = 4.4\%$: $a_{\overline{13}|} = 9.742306$, so $P = \dfrac{\text{PV}}{a_{\overline{13}|}} = \dfrac{46763.07}{9.742306}\;= 4800.0000$.

Answer
The answer is 4800.0000, option (A).

How to Solve Annuities — solving for the payment or the term of a level annuity Questions on Exam FM

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