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A certain sum amounts to тВ╣31,944 at a compound interest rate of 15% per annum in 2 years, with interest compounded every 8 months. What will be the amount payable (in тВ╣) on the same sum at the same rate and for the same time, if the interest is compounded yearly?
33,001
32,510
32,113
31,740 Question ID : 441009573563 Option 1 ID : 4410092249375 Option 2 ID : 4410092249373 Option 3 ID : 4410092249374 Option 4 ID : 4410092249372 Status : Answered Chosen Option : D
31,740 Question ID : 441009573563 Option 1 ID : 4410092249375 Option 2 ID : 4410092249373 Option 3 ID : 4410092249374 Option 4 ID : 4410092249372 Status : Answered Chosen Option : D
Since the time period is 2 years (24 months) and compounding is every 8 months, the number of cycles n=24/8=3. The rate per cycle is (15/12)├Ч8=10%. Calculate the effective interest multiplier (1.1)3=1.331 and solve for P.
Final amount A = 31,944, Rate R = 15% per annum, Time T = 2 years, compounding frequency = 8 months.
A=P(1+100rтАЛ)n
Since the time period is 2 years (24 months) and compounding is every 8 months, the number of cycles n=24/8=3. The rate per cycle is (15/12)├Ч8=10%. Calculate the effective interest multiplier (1.1)3=1.331 and solve for P.
Students often use the annual rate 15% directly instead of converting it to the periodic rate for 8 months, which is (15/12)├Ч8=10%.
Calculate the effective rate and number of cycles
Since the interest is compounded every 8 months, in 2 years there are n=824тАЛ=3 cycles. The rate for 8 months is r=1215%тАЛ├Ч8=10%.
r=10%,n=3
Calculate the Principal (P)
Using the compound interest formula 31944=P(1+0.10)3, we get 31944=P(1.331). Solving for P gives P=31944/1.331=24000.
P=24000
Calculate Amount with yearly compounding
For yearly compounding for 2 years at 15%, the amount is A=24000(1+0.15)2. This equals 24000├Ч1.3225=31740.
A=24000├Ч(1.15)2=31740
D is correct because the principal is calculated as 24,000, and compounding yearly at 15% for 2 years results in an amount of 31,740.
This logic is identical to effective rate calculations in EMI installments and bank recurring deposits.
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