Question

Calculate the amount and compound interest on

(a ) $Rs10800$ for $3$ years at $12\frac{1}{2}\%$ per annum compounded annually.

(b) $Rs18000$ for $2\frac{1}{2}$ years at $10\%$ per annum compounded annually.

(c) $Rs.62500$ for $1\frac{1}{2}$ years at $8\%$ per annum compounded half yearly.

(d) $Rs.8000$ for $1$ year at $9\%$ per annum compound half yearly.

(You could use the year by year calculation using SI formula to verify)

(e) $Rs.10000$ for $1$ year at $8\%$ per annum compounded half yearly.

Answer 1

(a)Principal (P) = Rs10, 800

Rate(R) $=12\frac{1}{2}\%=\frac{25}{2}\%$ (annually)

Numberof years (n) = 3

Amount, $A=P[1+\frac{R}{100}{]}^n$

$=Rs.\left[10800\right(1+\frac{25}{200}{)}^3]$

$=Rs.\left[10800\right(1+\frac{1}{8}{)}^3]$

C.I.= A − P = Rs (15377.34 − 10800) = Rs 4,577.34

(b)Principal (P) = Rs18,000

Rate (R) = 10% annual

Numberof years (n) =

Theamount for 2 years and 6 months can be calculated by firstcalculating the amount for 2 years using the compound interestformula, and then calculating the simple interest for 6 months on theamount obtained at the end of 2 years.

Firstly,the amount for 2 years has to be calculated.

Bytaking Rs 21780 as principal, the S.I. for the next year will be calculated.

∴Interest for the first 2 years = Rs (21780 − 18000) = Rs 3780

Andinterest for the nextyear= Rs 1089

∴Total C.I. = Rs 3780 + Rs 1089 = Rs 4,869

A =P + C.I. = Rs 18000 + Rs 4869 = Rs 22,869

(c)Principal (P) = Rs62,500

Rate= 8% per annum or 4% per half year

Numberof years =

Therewill be 3 half years inyears.

C.I.= A − P = Rs 70304 − Rs 62500 = Rs 7,804

(d)Principal (P) = Rs8000

Rateof interest = 9% per annum or %per half year

Numberof years = 1 year

Therewill be 2 half years in 1 year.

C.I.= A − P = Rs 8736.20 − Rs 8000 = Rs 736.20

(e)Principal (P) = Rs10,000

Rate= 8% per annum or 4% per half year

Numberof years = 1 year

Thereare 2 half years in 1 year.

C.I.= A − P = Rs 10816 − Rs 10000 = Rs 816