Question 1173170: 5. What sum must be deposited today at 18% per year compounded monthly if the goal is to a compound amount of $50, 00 six years from today? How much interest will be earned during this period?
Question no 03:
1. Determine the present value of a series of 60 monthly payments of $2,500 each which begins 1 month from today. Assume interest of 12 percent per year compounded monthly.
2.
3.
Determine the present value of a series of 36 monthly payments of $5,000 each which
begins 1 month from today. Assume interest of 18 percent per year compounded
monthly
A person wants to buy a life insurance policy which would yield a large enough sum of money to provide for 20 annual payments of $50,000 to surviving members of the family. The payments would begin 1 year from the time of death. It is assumed that interest could be earned on the sum received from the policy at a rate of 8 percent per year compounded annually.
(a) What amount of insurance should be taken out so as to ensure the desired annuity? (6) How much interest will be earned on the policy benefits over the 20-year period?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's tackle each of these financial calculations step-by-step.
**Question 1: Lump Sum Deposit for Future Value**
1. **Identify the variables:**
* Future value (FV): $50,000
* Interest rate per year (r): 18% or 0.18
* Compounding frequency (n): Monthly, so 12 times per year
* Interest rate per period (i): r/n = 0.18 / 12 = 0.015
* Number of years (t): 6
* Total number of periods (N): t * n = 6 * 12 = 72
2. **Use the present value formula:**
* PV = FV / (1 + i)^N
3. **Plug in the values:**
* PV = $50,000 / (1 + 0.015)^72
* PV = $50,000 / (1.015)^72
* PV = $50,000 / 2.930491879
* PV = $17,061.85 (approximately)
Therefore, approximately $17,061.85 must be deposited today.
4. **Calculate the interest earned:**
* Interest = FV - PV
* Interest = $50,000 - $17,061.85
* Interest = $32,938.15 (approximately)
Therefore, approximately $32,938.15 in interest will be earned.
**Question 3.1: Present Value of an Annuity (Monthly Payments, 12% Interest)**
1. **Identify the variables:**
* Payment (PMT): $2,500
* Number of payments (N): 60
* Interest rate per year (r): 12% or 0.12
* Compounding frequency (n): Monthly, so 12 times per year
* Interest rate per period (i): r/n = 0.12 / 12 = 0.01
2. **Use the present value of an ordinary annuity formula:**
* PV = PMT * [(1 - (1 + i)^-N) / i]
3. **Plug in the values:**
* PV = $2,500 * [(1 - (1 + 0.01)^-60) / 0.01]
* PV = $2,500 * [(1 - (1.01)^-60) / 0.01]
* PV = $2,500 * [(1 - 0.5504495) / 0.01]
* PV = $2,500 * [0.4495505 / 0.01]
* PV = $2,500 * 44.95505
* PV = $112,387.63 (approximately)
Therefore, the present value is approximately $112,387.63.
**Question 3.2: Present Value of an Annuity (Monthly Payments, 18% Interest)**
1. **Identify the variables:**
* Payment (PMT): $5,000
* Number of payments (N): 36
* Interest rate per year (r): 18% or 0.18
* Compounding frequency (n): Monthly, so 12 times per year
* Interest rate per period (i): r/n = 0.18 / 12 = 0.015
2. **Use the present value of an ordinary annuity formula:**
* PV = PMT * [(1 - (1 + i)^-N) / i]
3. **Plug in the values:**
* PV = $5,000 * [(1 - (1 + 0.015)^-36) / 0.015]
* PV = $5,000 * [(1 - (1.015)^-36) / 0.015]
* PV = $5,000 * [(1 - 0.580083) / 0.015]
* PV = $5,000 * [0.419917 / 0.015]
* PV = $5,000 * 27.99446
* PV = $139,972.30 (approximately)
Therefore, the present value is approximately $139,972.30.
**Question 4: Life Insurance Policy (Annuity)**
1. **Identify the variables:**
* Payment (PMT): $50,000
* Number of payments (N): 20
* Interest rate per year (r): 8% or 0.08
* Compounding frequency (n): Annually, so 1 time per year
* Interest rate per period (i): r/n = 0.08 / 1 = 0.08
2. **Use the present value of an ordinary annuity formula:**
* PV = PMT * [(1 - (1 + i)^-N) / i]
3. **Plug in the values:**
* PV = $50,000 * [(1 - (1 + 0.08)^-20) / 0.08]
* PV = $50,000 * [(1 - (1.08)^-20) / 0.08]
* PV = $50,000 * [(1 - 0.2145482) / 0.08]
* PV = $50,000 * [0.7854518 / 0.08]
* PV = $50,000 * 9.8181475
* PV = $490,907.38 (approximately)
(a) Therefore, the amount of insurance should be approximately $490,907.38.
(b) **Calculate the total payments:**
* Total payments = PMT * N = $50,000 * 20 = $1,000,000
(c) **Calculate the total interest earned:**
* Total interest = Total payments - PV
* Total interest = $1,000,000 - $490,907.38
* Total interest = $509,092.62 (approximately)
Therefore, the interest earned will be approximately $509,092.62.
Answer by ikleyn(52756)  (Show Source):
You can put this solution on YOUR website! .
Regarding the post by @CPhill:
Do not trust to calculations by @CPhill: I checked them,
and I found that they all are  from to be accurate,
from to be precise and from to be correct.
Regarding your post:
NEVER submit more than one problem/question per post.
It is PROHIBITED by the rules of this forum,
and those who VIOLATE these rules, work AGAINST their own interests.
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In other words, it is a greatest degree of stupidity
to post many problems/questions in one post.
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