Verified answer

Principal P=Rs.4,000. Since the interest is compounded half-yearly the number of conversion periods in 1½years are 3. Also the rate of interest per

conversion period (6 months) is 10% × 1/2 = 5%(0.05 in decimal).

Thus the amount A_n (in Rs.) is given by

A_n = P(1+i)^n

A_3 = 4,000(1+0.05)_3

= 4,630.50

The compound interest is therefore Rs. (4,630.50−4,000)

Answer:

• Compound Interest is Rs 630.5

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Step-by-step explanation:

Given : A sum of money of Rs.4000 is lent for 1.5 years at the rate of 10 % per annum Compounded Half-yearly

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To Find : Compute the Compound Interest

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SolutioN :

[tex] \dag \; {\underline{\underline{\sf{ \; Formula \; Used \; :- }}}} [/tex]

• [tex] {\underline{\boxed{\pink{\sf{ C.I = P \bigg\lgroup 1 + \dfrac{R}{200} \bigg\rgroup^{2n} - P }}}}} [/tex]

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Where :

• C.I = Compound Interest
• P = Principal
• R = Rate
• n = Time

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[tex] \dag \; {\underline{\underline{\sf{ \; Calculating \; the \; Interest \; :- }}}} [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = P \bigg\lgroup 1 + \dfrac{R}{200} \bigg\rgroup^{2n} - P } \\ \\ [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = 4000 \bigg\lgroup 1 + \dfrac{10}{200} \bigg\rgroup^{2 \times 1.5} - 4000 } \\ \\ [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = 4000 \bigg\lgroup 1 + \dfrac{10}{200} \bigg\rgroup^{3} - 4000 } \\ \\ [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = 4000 \bigg\lgroup 1 + \cancel\dfrac{10}{200} \bigg\rgroup^{3} - 4000 } \\ \\ [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = 4000 \bigg\lgroup 1 + \cancel\dfrac{5}{100} \bigg\rgroup^{3} - 4000 } \\ \\ [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = 4000 \bigg\lgroup 1 +0.05 \bigg\rgroup^{3} - 4000 } \\ \\ [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = 4000 \bigg\lgroup 1.05 \bigg\rgroup^{3} - 4000 } \\ \\ [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = 4000 \times 1.157625 - 4000 } \\ \\ [/tex]

[tex] \; \; :\implies \; \; \tt { C.I = 4630.5 - 4000 } \\ \\ [/tex]

[tex] \; \; :\implies \; \; {\underline{\boxed{\purple{\tt { C.I = Rs. \; 630.5 }}}}} \; \bigstar \\ \\ [/tex]

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❛❛ Compound Interest is Rs 630.5 ! ❜❜ ‎

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