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:单项选择题
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:单项选择题

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:单项选择题

类似问题

Simple interest at a rate of 6% per annum is paid on an investment of $1,500. The term of the investment is chosen so that the total interest earned is at least $540. The minimum term for this investment, to the nearest month, is:

Simple interest at a rate of 6% per annum is paid on an investment of $1,500. The term of the investment is chosen so that the total interest earned is at least $540. The minimum term for this investment, to the nearest month, is:

The amount which should be invested at 4.5% per annum simple interest, if you require $15 700 in three years’ time, is closest to:

The amount which should be invested at 4.5% per annum simple interest, if you require $15 700 in three years’ time, is closest to:

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:

The simple interest payable on an initial investment of $5000 invested at 6% per annum for three years will be:

What is the future value of $124.49 after earning simple interest for five years at an annual rate of 10%?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单