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1) Westin Lord Braking Company invested $150,650 in a fund at an interest rate of 11% compounded monthly. At the end of 5 months, the company’s investment advisor transferred these funds to another investment that was yielding 13% compounded monthly. Calculate the amount by which the fund grew at the end of 15 months from the initial investment.

Solution:

Initial investment= $150,650

Interest rate = 11% compounded monthly

Time= 5 months

Amount received after 5 months = Investment (1 + rate)^n

                                                =$150,650 ( 1+0.11)^5

                                                =$150,650* (1.685)

                                                =$253,845.25

New investment= $253,845.25

Interest rate = 13% compounded monthly

Time= 10 months

Amount received after 5 months = Investment (1 + rate)^n

                                                =$253,845.25 ( 1+0.13)^10

                                                =$253,845.25* (3.39)

                                                =$860535.398

2) Amanda won a lottery that would pay her $5,000 in a year and it $10,000 in two years. If the     lottery company had another option where she could get an upfront amount now and another $7,000 in one year, calculate the upfront amount that she would receive now from the second option, assuming that money is worth 2% compounded semi-annually.

Solution:

Present value of 2nd payout =?

rate of interest = 0.02,

Total compounding = 2,

Term = 1,

Final value of 2nd payout = $7000

now,

7000 = pv(1+(0.02/2))2

present value of 2nd payout = $6862.07

So,

Total payout – pv of 2nd payout = initial payout
$15000 – $6862.07 = $8137.93

A = p(1 + r/n)rt
8000 = p(1 + 0.02/2)2(2)
8000 = p(1 + 0.01)4
8000 = p(1.01)4
8000 ≈ p(1.0406)
7687.84 ≈ p

3) Zoe started investing $700 at the end of every month into an RRSP that has an interest rate of 4% compounded semi-annually. Three years later, the interest rate on her RRSP increased to 5% compounded monthly and remained the same thereafter. What is the accumulated value of the RRSP after seven years?

Solution:

n = no. of payments = 12*3=36
I= interest = 4%
Present value=0 in RRSP
Monthly payment (PMT) = $700

P/Y = 12

C/Y=2

A = PMT{(1+i)^n -1}/i
= $700 {(1+0.04)^36 -1}/0.04
=$54250

Now,

Rate=5% compounded monthly

Next 4 years

A = PMT{(1+i)^n -1}/i
= $700 {(1+0.05)^48 -1}/0.05
=$131600

Total accumulated value

= $54250+$131600+Intrest on $54250 for 4 years compounded monthly by 5 %
=$54250+$131600+$11983.57
=$197833.57

4) Since the birth of her daughter, 16 years ago, Solange has deposited $50 at the beginning of every month into an RESP. The interest rate on the plan was 4.8% compounded monthly for the first 8 years and 4.2% compounded monthly for the next 8 years. Calculate the value of the fund today (the end of a 16-year term). How much of this is interest?

Solution:

RESP

FV = C [ (1+i)^n-1]/I

= $50 [ (1+0.048)^96-1]/0.048

= $5837.77

Now again for 8 years at 4.2 rate

= $50 [ (1+0.042)^8-1]/0.042

Total fund =$13857.35

Intrest = fund- deposit

=$13857.35-$9600

=$4257.35

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