Question

For each question below, provide well-organized solutions showing all required steps. While calculators may be used for numerical calculations, other mathematical steps must be shown and justified in your written solutions and specific marks may be allocated for these steps. Be sure to demonstrate your understanding of the grade 11 course material by justifying your answers using the knowledge and skills learned in our class.

1. What interest rate, compounded semi-annually is needed for a $500 investment to increase to $634.12 after 6 years?

2. Charles pays $45 for a car stereo and borrows the remaining amount. The loan payments are $25 per month for 1 year. The interest rate is 18.6% / a compounded monthly. What was the selling price of the car stereo?

 

Answer 1

1)

Working:
we need to find the interest rate; thus we use the RATE function in excel (I/Y function in financial calculator)

= RATE( nper, PMT, PV, FV)

 

Here

Nper, period = 6 years*2 = 12

PMT, payment = 0

PV, present value = - $500

FV, future value = $634.12

 

Thus we type in the following in any excel cell

= RATE(12,0,-500,0634.12)

And the answer is 2.0000%

 

This is semi-annual rate

Annual rate = 2.0000%*2 = 4.0000%

 

Thus the interest rate here is 4.0000%.

 

2)

Working:
We use the PV function here

=PV(rate, nper, PMT, FV)

Here

Rate = 18.6%/12 = 1.55%

Nper, period = 1 years*12 months = 12

PMT, payment = $25

FV, future value = $0

 

Thus we type in the following in any excel cell

=PV(1.55%,12,-25,0)

And the answer is $ 271.84

 

Plus we also add the Lump-sum amount of $45 that we pay

Total Present value of payments = $271.84 + $45.00

                                                           = $ 316.84

 

Thus the Car stereo would cost $316.84.

1. Thus the interest rate here is 4.0000%.

2. Thus the Car stereo would cost $316.84.