Question

find the get back and compound interest on rs 50000 for 1 1\2 years at 4% per annum compounded half yearly​

Answer 1

Answer:

int: The amount can be calculated using the given data and the formula:

A=P(1+R100)t where,

A = Amount

P = Principal

R = Rate

T = Time

Remember to half the rate and double the time as the principal is compounded half-yearly.

Then, the compound interest can be calculated using the relationship:

Amount = Principal + Compound Interest

Complete step-by-step answer:

Given:

Principal (P) = Rs. 5000

Rate (R) = 8 %

As it is compounded half yearly, the rate will reduce to half

R=82%

R = 4 %

Time (t) = 1 year 6 months

= (1+12)yrs

(∵12m=1yr6m=112×66m=12yrs)

= 32yrs

As it is compounded half yearly, the time will be doubled:

t=2×32yrs

T = 3 yrs.

Substituting these values in the formula of Amount, we get:

A=P(1+R100)t

A=5000(1+4100)3

A=5000(104100)3

A=5000×104100×104100×104100

A = 5624.32

The amount is equal to Rs. 5624.32

Now,

Amount = Principal + Compound Interest

Compound Interest = Amount – Principal

Substituting the values, we get:

Compound Interest = 5624.32 – 5000

Compound Interest = 624.32

Therefore, the compound interest is Rs. 624.32 on Rs. 5000 if it is compounded half yearly for 1 year 6 months at 8 % per annum.

Note: We make the respective changes when compounded half-yearly because:

Rate is halved. The rate is generally given for a year (per annum) but when we require for half-yearly, the per annum rate is also reduced to half.

Time is doubled.When we talk about half a year (6 months), it occurs twice every year (6 + 6 = 12) and hence the time is doubled.