Problem 4.LO1.20 (similar to) Question Help Uriah Heep celebrated his 18th birth
ID: 1171192 • Letter: P
Question
Problem 4.LO1.20 (similar to) Question Help Uriah Heep celebrated his 18th birthday by opening a savings account at the Thames River Bank and depositing $3,200. He continued to deposit the same amount on every subsequent birthday until he was 33 years old. After depositing $3,200 on his 33rd birthday Uriah decided to abandon his savings plan. He never saved again, but he left the accumulated savings in the bank account. The bank paid an interest rate of 14%. When Uriah turned 65, he withdrew the money from the bank. What was the amount of his withdrawal? What was the amount of Uriah's withdrawal when he turned 65? S (Round to the nearest cent)Explanation / Answer
Solution to problem 4.LO1.20:
This is a future value of annuity due for the first 16 years and then single payment for the next 31 years.
First we will calculate the future value of the annuity due for the first 16 years
PMT = $3,200
Rate (r) = 14%
Years (n) = 16 years (from his 18th birthday to 33rd birthday)
FV annuity due = PMT {[(1+r)n – 1]/r} * (1 + r)
= 3,200 {[(1 + 0.14)16 – 1]/0.14} * (1 + 0.14)
= $185,976.3245
Now, we will calculate the future value of a single amount for the remaining 31 years
AMT = $185,976.3245
Rate (r) = 14%
Years (n) = 31 years (from his 34th birthday to 64th birthday)
FVsingle amount = PMT (1 + r)n
= 185,976.3245 (1 + 0.14)31
= $10,802,096.48
The amount of Uriah’s withdrawal when he turned 65 was $10,802,096.48
Solution to problem 4.LO2.23
Monthly payment (M) = $323
Annual interest rate (i) = 18.5%
Amount payable (A) = $15,500
M = A / [1 – 1/(1 + i/12)n] / (i/12)
323 = 15,500 / [1 – 1/(1 + 0.185/12)n] / (0.185/12)
15500/323 = [1 – 1/1.01542n] / 0.01542
1 – 1/1.01542n = 47.98762 * 0.1542
1.01542-n = 1 - 0.74
1.01542n = 3.8462
n log 1.01542 = log 3.8462
n = 88.0277 months
It will take 88.0277 months to pay off the credit card balance.
Solution to problem 4.LO4.36
Monthly payment (M) = $253.25
Monthly interest rate (i) = 0.95%
Amount payable (A) = $8,566.73
M = A / [1 – 1/(1 + i)n] / i
253.25 = 8566.73 / [1 – 1/(1 + 0.0095)n] / 0.0095
1 – 1.0095-n = 0.3214
1.0095n = 1.4735
n log 1.0095 = log 1.4735
n = 41 months
It will take Angela 41 months to pay off the debt.