Question

The formula for determining interest compounded monthly is A = P(1 + r/12 )^12t, where A represents the amount invested after t years, P the principal invested, and r the interest rate. Jimmy invests $1,000 at an interest rate of 10% for 3 years, while Jenny invests $1,000 at an interest rate of 5% for 6 years. Determine the amount of return gained by Jimmy and Jenny. In complete sentences, summarize your results.

Answer 1

since it was compounded annually just sub in the values: A= (1000)(1.1)^3, AND A= (1000)(1.05)^6, compare the two values

Answer 2

what does that mean ?

Answer 3

what part are you confused about

Answer 4

how did you get your numbers like 1.1

Answer 5

1+r
= 1 +10%
=1+0.1
=1.1

Answer 6

A= (1000) (1 + 10/12) ^12(3) ?

Answer 7

is it like that ?

Answer 8

no, as you don't need to divide by 12, as everything is compounded annually

Answer 9

okay ! so what do I do now with
A= (1000)(1.1)^3, AND A= (1000)(1.05)^6

Answer 10

the formula for compound interest is a=p(1+r)^n, where a= interest earned, p= principle, basically what you put in, r= the rate of the interest in decimal place and n= no of years term is invested

Answer 11

yeah that is true, sorry misread the question

Answer 12

okay ! so what do I do now with
A= (1000)(1.1)^3, AND A= (1000)(1.05)^6

Answer 13

The question makes it clear the the interest is compounded monthly.
The annual interest rate must be expressed as a decimal to use it in the formula. So 10% becomes 0.1 and the monthly interest rate is 0.1/12.
Jimmy's return is found by the calculation
\[A=1000(1+\frac{0.1}{12})^{(3\times12)}\]

Answer 14

Note that the formula given in the question must be used.

Answer 15

ooh okay ! & now what do I do ?

Answer 16

First calculate the sum of the terms inside the brackets, then raise that sum to the power of 36. Next multiply the result by 1000.

Answer 17

1,348.18
?

Answer 18

Good work! .Your result is correct

Answer 19

okay so when I add both numbers, I get $18,900 .41 + $1,348.18 = $20,248.58 !

Answer 20

Where did you get $18,900.41 from???

Answer 21

the second one !
A= (1000)(1 + 0.5/12)^72 = 18,900 .41

Answer 22

right ?

Answer 23

Not really. Jenny's return is found from
\[A=1000(1+\frac{0.05}{12})^{72}\]
The annual interest rate of 5% is 0.05 expressed as a decimal/

Answer 24

so this ? $ 1,348.18 + $1,348.18 = $2,697.19

Answer 25

My calculation for Jenny's return came to $1349.02. The summary of the results needs to make the following point:
Jenney's investment at half the interest rate and double the investment term of Jimmy's made only a slightly higher return. Obviously Jimmy made the better investment.

Answer 26

can you type how you did that ?

Answer 27

Item Jenny Jimmy
Investment $1000 $1000
Annual rate 5% 10%
Investment period 6 years 3 years
Return $1349.02 $1348.18