With slight modifications, the basic formula can be made to deal with compounding at intervals other than annually.
Since the compounding is done at six-monthly intervals, 4 per cent (half of 8 per cent) will be added to the value on each occasion.
Hence we use r = 0.04. Further, there will be ten additions of interest during the five years, and so n = 10. The formula now gives:
V = P(1 + r)10 = 5,000 x (1.04)10 = 7,401.22
Thus the value in this instance will be £7,401.22.
In a case such as this, the 8 per cent is called a nominal annual
rate, and we are actually referring to 4 per cent per six months.
I=prt
I=prt
I=prt
Exact interest, I= prt = $8000 × 0.085 × 90/365 = 167.67
Ordinary Interest, I= Prt = $8000 x 0.085 x 90/360 = 170
Let time period of S.I. be T years.
Then for a principal amount, say P,
ATQ, as, S.I. = C.I. for rate =10%p.a. and
time for C.I. = 2(P x 10 x T)/100 = P{[ (100+10)/100 ]2-1}T/10 = [ 110/100 ]2?1 = [(11/10)2?1] = (121-100)/100T/10 = 21/100T = 21/10 = 2.1 years
It is given that the initial amount invested in scheme A is Rs P at 10%per Annum S.I. =PTR/100 = P x 10 x 2/100 Now the total amount after 2 years is = 1.2P New Rate of interest = 12% per annum Time = 5 years S.I for next 5 years when new principal amount is 1.2 P = 1.2Px12x5/100 = 0.72P Total amount after 5 years at 12% per annun = 1.72P Given that 1.72P - 1.2P = 1300 P = 1300/0.52 P = Rs. 2500
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