Answer:
Explanation:
To find the future value and the compound interest paid on the loan, we can use the compound interest formula1:
A=P(1+r/n)nt
where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
Plugging in the given values, we get:
A=1200(1+0.07/1)1×3
A=1200(1.07)3
A=1459.69
The future value of the loan is $1459.69. The compound interest paid on the loan is the difference between the amount and the principal:
CI=A−P
CI=1459.69−1200
CI=259.69
The compound interest paid on the loan is $259.69.
To compare the compound interest with simple interest for the same period, we can use the simple interest formula2:
I=Prt
where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.
Plugging in the given values, we get:
I=1200×0.07×3
I=252
The simple interest paid on the loan is $252. The difference between the compound interest and the simple interest is:
CI−I=259.69−252
CI−I=7.69
The compound interest is $7.69 more than the simple interest for the same period. This means that the farmer pays more interest when the interest is compounded annually than when it is calculated simply.