Question

can someone please help me answer question D. Than you :)

Question 1 Jesslyn inherited $10 000 from a relative, and is considering investing the money in a savings account. She sees the following accounts advertised BANK ACCOUNT Trust Bank 2.75% per annum simple interest 25% per annum compound interest, Honest Bank compounding annually a. How much would her investment be worth after 5 years. i. in Trust Bank? ii. in Honest Bank? b. At the end of which year would the investment reach at least 512 000 in Trust Bank? C. Jesslyn would like to go travelling overseas in 5 years (from when she initially invests). She has calculated that she will need $15 000 to fund this. How much extra on top of the inheritance would she need to invest intially in honest Bank to achieve this? Give your answer correct to the nearest hundred dollars. d. Use your calculator to answer the following:

Answer 1

a) Trust Bank:

Money Invested =$ 10,000

After 5 years the Money will become as per below formula:

FV=PV+5*Annual Simple Interest

FV=10,000+5*10,000*2.75/100

Fv=10,000+1375=$11375

Honest Bank:

FV=PVx(1+r)n

FV=10,000*(1+2.5/100)5

FV=$11314.08213

b) FV=PV+5*Annual Simple Interest

Here FV=12,000

PV=10,000

r=2.75%

n=?

12,000=10,000+10000*n*2.75/100

n=7.2727 years.

c) As we calculated in question one that future value of 10,000 in honest bank after 5 years=$11314.08213

Now she needs 15,000 at the end of year 5, so she is short of =15,000-$11314.08213=$3685.918

Now this is the FV of extra amount she will have to invest over and above 10,000 at time=0 so that the amount become $3685.918

So applying the formula:

3685.918=PV*(1+2.5/100)^5

PV=$3257.814, approx 3300 therefore Jesslyn will have to invest $3300 extra aprt from 10,000 so that the total value becomes 15,000 at the end of 5 year.

d) For the investments of Honest bank to become greater than trust bank:

10000+10000*t*2.75/100=10000*(1+2.5/100)^t

1+0.0275t=(1.025)^t

After Solving t is approx=8.571 years

Value of the investments become:

=10000+10000*t*2.75/100=10,000+10,000*8.571*2.75/100=$12357.025

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