Question

4. $10,000 is deposited in a savings account earning 1.75% simple interest.

What is the future value (nearest penny) of the $10,000 after 5 years?

What is the future value after 5 years if the same account earns 1.75% interest compounded annually?  

5. You borrow $2000 on March 20 at 15% simple interest.  

a. How much interest (to the nearest penny) accrues by September 20 (180 days later). Assume ordinary interest.  

b. What is the total amount that you must repay?

6. A car has an advertised price of $22,000 cash or $650 per month for 4 years. If you pay the $650 per month for 4 years, what is the total amount you would be paying for the car?

7. If I = Prt and I = $398.90, r = 9.85% and t = 1 year, how much is P (to the nearest dollar)?  

8. If a loan is held for 180 days, then t is about: A. 180   B. 1/2   C. 1/4   D. 3  

Please show work. Thank you.

Answer 1

4.

Future value = P (1+ rt)

P = Principal = $ 10,000

r = Rate of interest = 1.75 % or 0.0175 p.a.

t = Time in years = 5 years

Future value = $ 10,000 x (1+ 0.0175 x 5)

                      = $ 10,000 x (1+ 0.0875)

                      = $ 10,000 x (1.0875)

                      = $ 10,875.00

Future value of $ 10,000 using simple interest after 5 years is $ 10,875.00

Future value = P x (1+ r) ^t

Future value = $ 10,000 x (1+ 0.0175) ⁵

                      = $ 10,000 x (1.0175) ⁵

                      = $ 10,000 x 1.09061656433662

                      = $ 10,906.1656433662 or $ 10,906.17

Future value of $ 10,000 using compound interest after 5 years is $ 10,906.17

a.

Ordinary interest = P x r x t

P = Principal = $ 2,000

r = Rate of interest = 15 % or 0.015 p.a.

t = Time in years = 180/365 years

Ordinary interest = $ 2,000 x 0.015 x 180/365

                               = $ 2,000 x 0.015 x 0.493150684931507

                               = $ 147.945205479452 or $ 147.95

b.

Total amount to pay = Principal + Interest = $ 2,000 + $ 147.95 = $ 2,147.95

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Total amount to pay for the car = EMI amount x Number of EMI

                                                       = $ 650 x 4 years x 12 months

                                                       = $ 31,200

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I = P x r x t

P = I/ (r x t)

= $ 398.90/ (0.0985 x 1)

    = $ 398.90/0.0985 = $ 4,049.7461928934 or $ 4,049.75

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180 = 180/360 = 0.5 or ½ years

Time in years, t is about ½ years