Question

13. Yufeng needs to have $3500 in 10 months' time If she can earn 6% simple interest, a) how much does she need to invest today? b) how much does she need to invest on July 31 if the $3500 is needed in 10 months?

Answer 1

a)

Answer: Amount to be invested today = $3333.33

Formula for calculating simple interest = P*N*R

Where,

P = Principal Amount

N = Number of moths

R = rate of interest

In this case we need $3500 in 10 months with interest rate of 6%

If we invest “X” today at interest rate of 6% it will be $3500

i.e. Principal amount (X) + Interest for 10 months will be $3500

Interest rate for 10 months will be = 6% *10/12

                                                =5%

Principal Amount + interest for 10 months = $3500                                           

X + (X *5%) = $3500

X +05X = $3500

1.05X = $3500

X = 3500 ÷ 1.05

=$3333.33

B) Answer : Amount to be invested today $3349.28

Since we are investing on the month end (31st July) for the month of July we won’t get any interest, we will get interest only for 9 months. In that case principal amount + 9 months interest will be $3500

i.e. Principal amount (X) + 9month interest at 6% will be $3500

9 month interest rate = 6 *9/12

                                    =4.5%

Principal Amount + interest for 9months = $3500

X + (X* 4.5%) = $3500

X + .045X =$3500

1.045X = $3500

X = 3349.28

Note

Amount to be invested is denoted as X (principal Amount)

In the part B of the problem an alternative view can be taken, that is 1st month from July 31st is completed on 30th august. Then in that case answer will be $3333.33 (i.e. 10 full months interest)