Question

A certain sum of money at compound interest amounts to 6600 in one year and to 7986 in three years. Find the sum and rate percent.​

Answer 1

Answer:

A certain sum of money at compound interest amounts to 6600 in one year and to 7986 in three years. The sum and rate percent are 6000 and 10% respectively.

Step-by-step explanation:

The compound interest accumulation formula is given by:

A = P(1 + i)ⁿ

P = Principal amount

i = rate of interest

n = time period

Substituting this in each of the cases we have:

6600 = P(1 + i)

7986 = P(1 + i)³

Rewriting the equations we have:

P =6600/(1 + i)

P= 7986/(1 + i)³

Equating the two values of P we have:

6600/(1 +i) =7986/(1 + i)³

(1 + i)³/(1 + i) = 7986/6600

(1 + i)² = 1.21

Getting square root on both sides we have:

1 + i = 1.1

i = 1.1 - 1

i = 0.10

i = 10%

Substituting the value of in any of the equations to get P, we have:

6600/(1.10) = 6000

The sum is 6000 and the rate percent is 10%.