7. Suppose you know you will need $20,000 in eight years. How much should you pu

Question

7. Suppose you know you will need $20,000 in eight years. How much should you put into an account paying 9.00% interest (compounding quarterly) so that you will have the $20,000 eight years from now?

8. Bernard deposits $16,000 in a savings account that compounds interest annually at an APR of 4%. Carla deposits $14,000 in an account that gives 5% compounded daily. Who will have more money after 5 years? Who will have more money after 20 years?
9. (Extra Credit challenge) If I want my $12,600 to grow to $20,000 in ten years, what interest rate do I need if the money is compounded monthly?
10. (super awesome challenge) How long will it take $10,000 to grow to $15,000 at 4% compounded monthly? Suppose you know you will need $20,000 in eight years. How much should you put into an account paying 9.00% interest (compounding quarterly) so that you will have the $20,000 eight years from now? 7. Bernard deposits $16,000 in a savings account that compounds interest annually at an APR of49. Carla deposits $14,000 in an account that gives 5% compounded daily. Who will have more money after 5 years? Who will have more money after 20 years? 8, Bernard Carla (Extra Credit challenge) If I want my $12,600 to grow to $20,000 in ten years, what interest rate do I need if the money is compounded monthly? 9. 10, (super awesome challenge) How long will it take $10,000 to grow to Si 5,000 at 4% compounded monthly?

Explanation / Answer

7). Interest = 9% compounded quarterly

So quarterely interest rate = 9/4 = 2.25%

In 8 years there are 8*4 = 32 quarters

After 8 years investment = $20,000

Therefore Present value of investment = FV/(1+r)n, where r is rate of return and n is number of periods

PV = 20,000/(1.0225)32 = 9813.05

8). Bernard deposit = $16,000

Interest rate = 4%

After five years value of investment = 16000*(1.04)5 = 19466.45

After twenty years value of investment = 16000*(1.04)20 = 35057.97

Carla deposits = 14000

Interest rate = 5% compounded daily

Daily interest = 5/365 = 0.014%

Therefore effective annual interest rate = (1+daily interest)365 - 1 = 5.13%

After 5 years investment = 14000*(1+0.0513)5 = 17976.05

After 20 years investment = 14000*(1+0.0513)20 = 38053.34

After 5 years Bernanrd will earn more and after 20 years carla will earn more.

9). Present value of mortgage = 12600

Future value = 20000

Time = 10 years

If money is compounded monthly then time is 10*12 = 120 months

Therefore 12600*(1+r)120 = 20000

Solving this value of r = 0.39%

So effective annual interst rate = (1+r)12 - 1 = 4.73%

10). Current value of investment = 10000

Future value = 15000

Interest rate = 4% compounded monthly

Monthly interest rate = 4/12 = 0.33%

So 10000*(1+0.0033)n = 15000

Solving this we get n as 122

So it will take 122 months for investment to grow i.e. 10 years and 2 months

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.