1.Calculate the amount obtained for the
following loans
a) RM 2,500 with interest 7.5% compounded
semi-annually for 6 years.(RM3888.64)
b) RM 750 with interest 2.25% compounded
quarterly for 8 months.(RM761.30)
c) RM 3,700 with interest 6.5% compounded
monthly for 8 years.(RM3863.41)
Answers
Given a) :- RM 2,500 with interest 7.5% compounded semi-annually for 6 years .
Answer :-
we know that, when rate is compounded Half - Yearly :-
- Half yearly Means Half of a year, when we Multiply it with 2 we will get a year .
So we can say that in this case :-
- Rate is Divided by 2.
- Time is Multiply by 2 . ( To make it a complete year).
so,
- Rate = (7.5/2)% per annum = 3.75% = (3.75/100) = 0.0375
- Time = 6 * 2 = 12 years .
then,
→ Amount = RM[1 + rate in decimal]^time
→ Amount = 2500[1 + 0.0375]¹²
→ Amount = 2500 * (1.0375)¹²
→ Amount = 2500 * 1.5554
→ Amount ≈ RM3888.64 (Ans.)
Given b) :- RM 750 with interest 2.25% compounded quarterly for 8 months.(RM761.30) .
Answer :-
we know that, when rate is compounded quarterly :-
- Rate is divided by 4 .
- Time is multiply by 4 .
so,
- Rate = (2.25/4) = (225/400) = (225/400) * (1/100) = 0.005625 .
- Time = 8 * 4 = 32 months = 2 years + 8 months = 2(8/12) = 2(2/3) = (8/3) years .
then,
→ Amount = 750[1 + 0.005625]^(8/3)
→ Amount = 750 * (1.005625)^(8/3)
→ Amount = 750 * 1.0150704
Amount ≈ RM761.30 (Ans.)
Hint for c) :- Divide rate by 12 and multiply time by 12 and put value in amount formula .
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