Question

Martin is offered an investment where for $ 6 comma 000 ​today, he will receive $ 6 comma 420 in one year. He decides to borrow $ 6 comma 000 from the bank to make this investment. What is the maximum interest rate the bank needs to offer on the loan if Martin is at least to break even on this​ investment

Answer 1

Answer:

7%

Explanation:

If Martin invest $6,000 today and receives $6,420 in one year, we can use the future value formula to determine the interest rate:

future value = present value x (1 + r)ⁿ

• future value = $6,420
• present value = $6,000
• n = 1
• r = ?

$6,420 = $6,000 (1 + r)

1 +r  = $6,420 / $6,000 = 1.07

r = 1.07 - 1 = 0.07 or 7%

In order to at least break even (no profit or no loss), Martin must get a loan that charges him a maximum of 7%

Answer 2

Answer: The maximum interest rate shall be 7%

Explanation: From the information given, if Martin were to invest a principal amount of $6000 at the present time, after a period of one year, he would have received a total of $6420. That means he is making an additional $420, which is actually the interest gained over the $6000 invested. The interest rate that would yield such an amount over $6000 is calculated by means of the simple interest formulae which is;

I = PRT/100

Where the principal (P) is 6000, the interest (I) is 420 and the time (T) is 1, rearranging the formulae to make R (rate of interest) the subject of the formulae, we now have;

(100 x I)/PT = R

(100 x 420)/6000 x 1 = R

42000/6000 = R

7 = R

Therefore the interest rate should be 7%