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A bank offers 5% compound interest calculated on half yearly basis.
A customer deposits 1600 each on 1st January and 1st July of a year.
Find the interest it would have gained at the end of the year
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Formulation of the problem is a bit strange, since it does not concretizes
at the end of which year it wants to get the interest/answer.
So, I will assume that it wants the interest at the end of the first year.
It is an Annuity Due saving plan. The general formula is
FV = , (1)
where FV is the future value of the account; P is the semi-annual payment (deposit);
r is the semi-annual effective rate presented as a decimal;
n is the number of deposits (= the number of years multiplied by 2, in this case).
Under the given conditions, P = 1600; r = 0.05/2 = 0.025; n = 1*2 = 2.
So, according to the formula (1), Future Value of the account at the end of the first year
FV = = 3321.
Note that the customer will deposit only 2*1600 = 3200 in two semi-annual payments.
So, the interest at the end of the first year is 3321 - 3200 = 121. ANSWER
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On Annuity Due saving plans, see the lessons
- Annuity Due saving plans and geometric progressions
- Find future value for an Annuity Due saving plan
in this site.
The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.