Question

A sum of rs.12500 is deposited for 1.5years,compounded half yearly.it amounts to rs.13000/-at the end of first year.find:
1) the rate of interest
2)final amount to nearest rupee

Answer 1

1) The rate of interest = 3.961%

2) Final amount after 1.5 years = ₹ 13257

Step-by-step explanation:

Rate of interest formula :

$r=n[(\frac{A}{P})^{\frac{1}{nt}}-1 ]$

Where r = rate of interest

n = number of compounding period (half yearly) = 2

A = Maturity amount (13,000)

P = principal amount (12,500)

t = time in years (1 year)

Now plug in values to the formula :

$r=2[(\frac{13000}{12500})^{\frac{1}{2\times1}-1}]$

  $=2[(1.04)^{0.5}-1]$

  = 2(1.01980390 -1)

  = 2 × 0.01980390

  = 0.0396078

  ≈ 3.961%

Now we will calculate the final amount after 1.5 year by this formula :

$A=P(1+\frac{r}{n})^{nt}$

   $=12500(1+\frac{0.03961}{2})^{2\times 1.5}$

   $=12500(1+0.019805)^{3}$

   = 12500 (1.019805)³

   = 12500 × 1.060599482

   = 13257.493525

   ≈ ₹ 13257

1) The rate of interest = 3.961%

2) Final amount after 1.5 years = ₹ 13257

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