Annual deposit savings

A person deposits 5,000 euros into a bank account at the beginning of each year for 10 years. He does not make any other deposits or withdrawals from the account. Determine the total amount saved at 8% compounded annually when interest is compounded annually.

Final Answer:

a₁₀ =  78227.44 eur

Step-by-step explanation:

$$\begin{gathered} a_0=5000 \\ q=100\%+8\%=1+\frac{8}{100}=1.08 \\ {a}_1=a_0\cdot q=5000\cdot 1.08=5400 \\ {a}_2=(a_1+a_0)\cdot q=(5400+5000)\cdot 1.08=11232 \\ {a}_3=(a_2+a_0)\cdot q=(11232+5000)\cdot 1.08=17530.56 \\ {a}_4=(a_3+a_0)\cdot q=(17530.56+5000)\cdot 1.08=24333.0048 \\ {a}_5=(a_4+a_0)\cdot q=(24333.0048+5000)\cdot 1.08\doteq 31679.6452 \\ {a}_6=(a_5+a_0)\cdot q=(31679.6452+5000)\cdot 1.08\doteq 39614.0168 \\ {a}_7=(a_6+a_0)\cdot q=(39614.0168+5000)\cdot 1.08\doteq 48183.1381 \\ {a}_8=(a_7+a_0)\cdot q=(48183.1381+5000)\cdot 1.08\doteq 57437.7892 \\ {a}_9=(a_8+a_0)\cdot q=(57437.7892+5000)\cdot 1.08\doteq 67432.8123 \\ {a}_{10}=(a_9+a_0)\cdot q=(67432.8123+5000)\cdot 1.08=78227.44\text{eur} \end{gathered}$$

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