Find the annual installment which will discharge a debt of Rs. 63840 i

1.	Find the annual installment which will discharge a debt of Rs. 63840 in 3 years at 8% p.a. compound interest –1). Rs. 23309.702).3). Rs. 29407.904). Rs. 29804.50
Answer» For CI: $(A = P{\left( {\;1\; + \frac{r}{{100}}\;} \right)^t})$ Where, A is the amount at the end of time t, P is the principal, t is time, r is rate Let the annual INSTALLMENT be a. For 1 YEAR, $({\rm{a}} = {P_1} \times {\left( {\;1 + \frac{r}{{100}}\;} \right)^1})$ For 2 YEARS $({\rm{a\;}} = {P_2} \times {\left( {\;1 + \frac{r}{{100}}\;} \right)^2})$ For 3 years $({\rm{a}} = {P_3} \times {\left( {\;1 + \frac{r}{{100}}\;} \right)^3})$ GIVEN, P1 + P2 + P3 = 63840 and r = 8% $(\Rightarrow \frac{a}{{1 + \frac{8}{{100}}}} + \frac{a}{{{{\left( {\;1 + \frac{8}{{100}}} \right)}^2}}} + \frac{a}{{\;{{\left( {1 + \frac{8}{{100}}} \right)}^3}}} = {\rm{\;}}63840)$ ⇒ a × (2.577 ) = 63840 ⇒ a = Rs. 24772.06

Find the annual installment which will discharge a debt of Rs. 63840 in 3 years at 8% p.a. compound interest –1). Rs. 23309.702).3). Rs. 29407.904). Rs. 29804.50

Answer»

For CI:

$(A = P{\left( {\;1\; + \frac{r}{{100}}\;} \right)^t})$

Where,

A is the amount at the end of time t,

P is the principal,

t is time,

r is rate

Let the annual INSTALLMENT be a.

For 1 YEAR,

$({\rm{a}} = {P_1} \times {\left( {\;1 + \frac{r}{{100}}\;} \right)^1})$

For 2 YEARS

$({\rm{a\;}} = {P_2} \times {\left( {\;1 + \frac{r}{{100}}\;} \right)^2})$

For 3 years

$({\rm{a}} = {P_3} \times {\left( {\;1 + \frac{r}{{100}}\;} \right)^3})$

GIVEN, P1 + P2 + P3 = 63840 and r = 8%

$(\Rightarrow \frac{a}{{1 + \frac{8}{{100}}}} + \frac{a}{{{{\left( {\;1 + \frac{8}{{100}}} \right)}^2}}} + \frac{a}{{\;{{\left( {1 + \frac{8}{{100}}} \right)}^3}}} = {\rm{\;}}63840)$

⇒ a × (2.577 ) = 63840

⇒ a = Rs. 24772.06

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