This is an actuarial science question Question: A person deposits $100 at the be

Question

This is an actuarial science question

Question: A person deposits $100 at the beginning of every year for 20 years with a simple interest. At the end of 20 years, the person's accumulated value is $2825 when invested with simple interest. What is the accumulated value when the investment occurs under compound interest?

My question is:

- How should we calculate the rate of simple interest?

-Is the simple rate same as a compound rate?

-Can we apply the annuity-due formula to calculate accumulated value under simple interest? if so, how should we apply it?

- If the deposits occur at the end of the year instead of at the beginning of the year, how should you calculate the simple interest rate?

Can you please answer me this question by mentioning appropriate formulas to use?

Thanks,

Explanation / Answer

Simple interest 136.25% (Accumulated value-Principal)/(years*principal)         2,93,38,39,447 Principal*(1+r)^years - Simple rate of interest rate on principal only So if 136.25% for 20 year than interest would be 136.25*20=2725% Principal amount is 100 Interest would be =100*2725% 2725 Total Value 2825 - Compound rate of interest is different from simple as in compound interest is also charged on interest Formula for that is Principal*(1+r)^years - No we can't apply annuity due formula Formula is= no of years *interest rate p.a* principal - If deposit occuer at the ens of the year simply dedcut one year like in present case year would be 19 (20-1)

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