For the following exercise, use the compound interest formula, A(t) = P 1 + r n nt , where money is measured in dollars. After a certain number of years, the value of an investment account is represented by the expression 10,950 1 + 0.03 2 24 . How many years had the account been accumulating interest? yr
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For the following exercise, use the
r |
n |
nt | |
where money is measured in dollars.
After a certain number of years, the value of an investment account is represented by the expression
0.03 |
2 |
24 | |
How many years had the account been accumulating interest?
yr
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- For each of the following situations involving annulties, solve for the unknown. Assume that interest is compounded annually and that all annulty amounts are received at the end of each period. (/= Interest rate, and n = number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) 1. 2. 3. 4. 5. Present Value 248, 196 442,750 650,000 175,000 Annuity Amount $ 5,000 80,000 60,000 155,040 8% 11% 10% n = 5 4 10 4To calculate how many years (n) an investment (P) must be kept in an account that earns interest at i%, in order to triple in amount, which of the following expressions should be used? (a) n = -P + F(P/F, i%, n) (b) n = [log (F/P)]/[log (1+ i%)] (c) n = [ In(– P +F)]/[In i%] (d) n = -F(1 + i%)PCompute the number of years (t) if future value (FV) = $5575, present value (FV) = $1812, and interest rate (r) = 9.1%,
- For each of the following situations involving single amounts, solve for the unknown. Assume that interest is compounded annually. (i= interest rate, and n = number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) 1. 2. 3. 4. 5. Present Value Future Value 80,000 94,000 50,000 200,000 $ $ $ $ $ 31,841 $ 15,762 $ 84,482 $ 13,291 i 7% 8% 9% n 9 16 10 15 1For each of the following situations involving single amounts, solve for the unknown. Assume that interest is compounded annually. (/= interest rate, and n=number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1. PV of $1. EVA of $1. PVA of $1. FVAD of $1 and PVAD of $1) 1. 2 3. 4. 5. Present Value Future Value 1 $ 36,600 $ 62,000 $ 28,644 $ 76,000 $ 11,758 $ 45,500 68.822 $ 155,000 13,796 $ $ 5% 7% 8% n 20 12 10If an investment of $2,000 grew to $2,520 in three periods, what is the interest rate at which the investment grew? Solve using both present and future value tables.
- All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or investment period. Each line on the following graph corresponds to an interest rate: 0%, 8%, or 16%. Identify the interest rate that corresponds with each line. VALUE (Dollars) Line A: 01 2 3 4 5 Line B: 6 B Line C: C 7 8 9 10 TIME (Years) Investments and loans base their interest calculations on one of two possible methods: the interest and the interest methods. Both methods apply three variables-the amount of principal, the interest rate, and the investment or deposit period to the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables.Compute the following with the data provided: (Show sufficient work with formulas used and all the steps involved ) A=$12, 500.00 per Quarter r=7.5% N=12 years Present Worth if the interest is compounded monthly? Future Value if the interest is compounded Quarterly: Present Worth if the interest is compounded continuously?For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (/= interest rate, and n= number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1. PV of $1. FVA of $1. PVA of $1. EVAD of $1 and PVAD of $1) 1. $ 2 3 4. 15 Present Value Answer is complete but not entirely correct. Annuity Amount 2.200 145,000 190,000 72.523 45,787 8,784 558,865 480,945 520,000 240,000 8% 1.0% 9% 2.5% 10% n= 5 4 30 8 4
- Compute the interest rate if future value (FV) = $8011, present value (FV) = $2685, and number of years (t) = 6.Example 1. Compound interest When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is, dx/dt = rx. (a) If $2000 is invested at 8%, compounded continuously, find an equation for the future value of the investment as a function of time t, in years. (b) How long will it take for the investment to double? (c) What will be the future value of this investment after 35 years?For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor. 1. In a future value of 1 table: a. b. C. a. b. Annual Rate C. 10% 12% 12% Annual Rate 12% 12% 8% Number of Years Invested Number of Years Invested 26 16 7 12 6 2. In a present value of an annuity of 1 table: (Round "Rate of Interest" answers to 1 decimal place, e.g. 4.5% and other answers to O decimal places, e.g 45.) 20 Number of Rents Involved 26 32 Compounded 28 Annually Quarterly Semiannually Frequency of Rents Annually Semiannually (a) Rate of Interest Quarterly % (a) Rate of Interest % % % % (b) Number of Periods % (b) Number of Periods