Question

1. Instructions: Read each item below. Use the PVIF and FVIF tables and the simple interest formula to help answer the items below.

1. Joel is going to put $2500 in a savings account at a local bank. The savings account will earn Joel 8% annually, simple interest. How much will Joel have in his account if he leaves the money there for 5 years? 10 years?
2. If Joel had put the $2500 in an account in which the interest compounded annually, how would his account balance differ from the balances in #1 (At 5 years and 10 years)
3. Cade has $5000 available to invest. He has found an opportunity to invest this money at 12% annually. If Cade left this money to grow at this rate (compounding) for 10 years, how much would he have at the end of the 10^th year?
4. If Cade were able to leave it for 15 years, what would the balance be?
5. Cameron wants to have $5000 for a down payment on a vehicle. He plans to purchase the vehicle in approximately 4 years (at the time he thinks he’ll need to get rid of his current vehicle). If he can earn 9% interest, how much must he deposit now in order to have the money in 4 years?
6. What would the present value of an account be if the future value is $20,000 and it has been compounding at a rate of 6% for the past 5 years?
7. What should Jeff be willing to invest now in order to have $20,000 in 15 years if his investment will compound at a rate of 10% annually.
8. Jordan wants to accumulate $1000 two years from now. If he can earn 6% on his investment, how much should he invest now?
9. Maria would like to know the difference in account values if she:
   1. Invested $10,000 for 5 years @ 8%, simple interest
   2. Invested $10,000 for 5 years @ 8%, compounding interest

Answer 1

#1. Simple Interest =

РxRx1/100

For 5 years

= 2500*8%*5 = $1000

Amount = Principal + Interest = 2500+1000 = $3500

For 10 years

= 2500*8%*10 = $2000

Amount = 2500+2000= $4500

#2. Amount at Compound Interest = P(1+R)^T

For 5 years

= 2500(1+8%)⁵ = $3673.32

For 10 years

= 2500(1+8%)¹⁰ = $5397.312

#3. Amount at the end of 10th year = 5000(1+12%)¹⁰ = $15,529.241

#4. Amount at the end of 15th year = 5000(1+12%)¹⁵ = $27,367.83

#5. We will calculate the present value of the payment to be made after 4 years -

=> Present Value = Future Value / (1+i)ⁿ = $5000 / (1+9%)⁴ = $3542.13

He will have to deposit $3542.13 now to have $5000 at the end of 4th year compounded annually.

#6. PV = $20,000 / (1+6%)⁵ = 14,945.163

#7. PV = $20,000 / (1+10%)¹⁵ = $4787.84 must be invested by Jeff now to get $20,000 at the end of 15th year.

If he gets 6% interest , then PV = $20,000 / (1.06)¹⁵ = $8345.30

#8. a. Amount at Simple Interest = 10,000 + 10,000*8%*5 = $14,000

b. At compound interest = 10,000(1+8%)⁵ = $14,693.28

Difference in the account values = $693.28