1. How much interest will be earned in the next year on an investment paying 11%

Question

1. How much interest will be earned in the next year on an investment paying 11% compounded annually if $100 was just credited to the account for interest?

2. Beginning today, a perpetuity of $7,200 per year, is said to offer a 14% interest rate. What is its present value?

3. What is the present value of the following payment stream, discounted at 9% annually: $2,800 at the end of year 1, $3,800 at the end of year 2, and $4,800 at the end of year 3?

4. How much principal is amortized with the first payment if a $67,000 is borrowed, to be repaid in three equal, annual payments with 9% interest?

5. What is the future value of $12,000 on deposit for 5 years at 6% simple interest?

6. How much should be deposited today in an account earning 5% annually to accumulate a 15% down-payment to use in purchasing a house one year from now, assuming that the house's current price is $22,000, and inflation will be 2%?

2. Beginning today, a perpetuity of $7,200 per year, is said to offer a 14% interest rate. What is its present value?

Explanation / Answer

1. Principal last year = $100 / 11%

= $909.09

Interest this year = ($909.09 + $100) * 11%

= $111

2. Present value = $7,200 / 14%

= $51,428.57

3. Present value = $2,800 / (1+9%) + $3,800 / (1+9%)2 + $4,800 / (1+9%)3

= $9,473.70

4. Annual payment = $67,000 * 9% * (1+9%)3 / [(1+9%)3 - 1]

= $26,468.67

Interest during first year = 9% * $67,000

= $6,030.00

Principal amortized in first year = $26,468.67 - $6,030.00

= $20,438.67

5. Future value = $12,000 + $12,000 * 6% * 5

= $15,600

6. Price of the house one year from now = $22,000 * (1+2%)

= $22,440

Down payment = 15% * $22,440

= $3,366

Deposit needed today = $3,366 / (1+5%)

= $3,205.71

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