Section 5.1 Simple and Compound Interest Page | 1

Section 5.1

Simple and Compound Interest

Section 5.1 Simple and Compound Interest Page | 2

Example 1. To buy furniture for a new apartment, Pamela Shipley borrowed $5000 at 8%

simple interest for 11 months. How much interest will she pay?

Example 2. Find the Future (maturity) value for each loan at simple interest.

(a) A loan of $2500 to be repaid in 8 months with interest of 4.3%.

(b) A loan of $11,280 for 85 days at 7% interest.

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Example 3. Alicia Rinke wants to borrow $8000 from Robyn Martin. She is willing to pay

back $8180 in 6 months. What interest rate will she pay?

Compound annually: 𝑚 = 1, so 𝑖 = 𝑟, 𝑛 = 𝑡

Compound semiannually: 𝑚 = 2, so 𝑖 =𝑟

2, 𝑛 = 2𝑡

Compound quarterly: 𝑚 = 4, so 𝑖 =𝑟

4, 𝑛 = 4𝑡

Compound monthly: 𝑚 = 12, so 𝑖 =𝑟

12, 𝑛 = 12𝑡

Compound daily: 𝑚 = 365, so 𝑖 =𝑟

365, 𝑛 = 2𝑡

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Example 4. Suppose $1000 is deposited for 6 years in an account paying 4.25% per year

compound annually.

(a) Find the compound amount.

(b) Find the amount of interest earned.

Example 5. Find the amount of interest earned by a deposit of $2450 for 6.5 years at 5.25%

compounded quarterly.

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Example 6. Suppose Susan Nassy invested $5000 in a savings account that paid quarterly

interest. After 6 years the money had accumulated to $6539.96. What was the annual interest

rate?

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Example 7. Joe Vetere needs to borrow money. His neighborhood bank charges 8% interest

compounded semiannually. An Internet bank charges 7.9% interest compounded monthly. At

which bank will joe pay the lesser amount of interest?

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Example 8. Stacey Sveum must pay a jump sum of $6000 in 5 years. What amount deposited

today at 6.2% compounded annually will amount to $6000 in 5years?

Example 9. Find the present value of $16,000 in 9 years if money can be deposited at 2%

compounded semiannually.

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Example 10. Suppose the $2450 is deposited at 5.25% compounded quarterly until it reaches

at least $10,000. How much time is required?

Example 11. Suppose the general level of inflation in the economy average 8% per year. Find

the number of years it would take for the overall level of prices to double.

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Example 12. Suppose that $2450 is deposited at 5.25% compounded continuously.

(a) Find the compound amount and the interest earned after 6.5 years.

(b) Find the effective rate.

(c) Find the time required for the original $2450 to grow to $ 10,000.

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