Simple interest at a rate of 7.5% per annum is paid on an investment of $1200.The term of the investment is chosen so that the total interest earned will be at least $460.The minimum term for this investment, to the nearest month, is:Single choice
A
a. 58 months
B
b. 50 months
C
c. 61 months
D
d. 62 months

Question

Simple interest at a rate of 7.5% per annum is paid on an investment of $1200.The term of the investment is chosen so that the total interest earned will be at least $460.The minimum term for this investment, to the nearest month, is:Single choice

A

a. 58 months

B

b. 50 months

C

c. 61 months

D

d. 62 months

BlackTom AI · Accepted Answer

Simple interest uses I = P · r · t, where I is interest, P the principal, r the annual rate (decimal), and t time in years.

Compute the annual interest factor first: P · r = 1200 × 0.075 = 90 (dollars per year).  
Solve for t in years: t = I / (P·r) = 460 / 90 = 46/9 = 5.111111... years.  (Intermediate: 460 ÷ 90 = 5 remainder 10 → 5 + 10/90 = 5.111111…)

Convert years to months: 5.111111... years × 12 months/year = (46/9) × 12 = 552/9 = 184/3 = 61.333333... months.

The question asks for the minimum term “to the nearest month.” Rounding 61.333... to the nearest whole month gives 61 months. Therefore the answer is 61 months.

Why this is correct: the exact minimum duration to reach $460 of simple interest is 61.333... months; applying the instruction “to the nearest month” requires standard rounding, which yields 61 months. (If the problem instead required the minimum whole number of months that ensures at least $460, one would choose 62 months, since 61 months yields only $457.50. But the phrasing “to the nearest month” directs rounding.)

Why the other choices are incorrect:
- 50 months and 58 months are well below the calculated 61.333... months and give substantially less than $460 interest.
- 62 months is the next whole month above the exact value (useful if rounding up to guarantee at least $460), but it is not the nearest month.

Final confirmation: the correct choice is c. 61 months.

Simple interest at a rate of 7.5% per annum is paid on an investment of $1200.The term of the investment is chosen so that the total interest earned will be at least $460.The minimum term for this investment, to the nearest month, is:Single choice

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