SECTION 5.7 Financial Models 345 5.7 Financial Models Now Work the ‘Are You Prepared?’ problems on page 351. • Simple Interest (Section A.8, pp. A67–A68) PREPARING FOR THIS SECTION Before getting started, review the following: OBJECTIVES 1 Determine the Future Value of a Lump Sum of Money (p. 345) 2 Calculate Effective Rates of Return (p. 348) 3 Determine the Present Value of a Lump Sum of Money (p. 349) 4 Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money (p. 350) THEOREM Simple Interest Formula If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed as a decimal, the interest I charged is = I Prt (1) 1 Determine the Future Value of a Lump Sum of Money Interest is money paid for the use of money. The total amount borrowed (whether by an individual from a bank in the form of a loan or by a bank from an individual in the form of a savings account) is called the principal . The rate of interest , expressed as a percent, is the amount charged for the use of the principal for a given period of time, usually on a yearly (that is, per annum) basis. Interest charged according to formula (1) is called simple interest . In problems involving interest, the term payment period is defined as follows. Annually: Once per year Semiannually: Twice per year Quarterly: Four times per year Monthly: 12 times per year Daily: 365 times per year* When the interest due at the end of a payment period is added to the principal so that the interest computed at the end of the next payment period is based on this new principal amount ( ) + old principal interest , the interest is said to have been compounded . Compound interest is interest paid on the principal and on previously earned interest. Computing Compound Interest A credit union pays interest of 2% per annum compounded quarterly on a certain savings plan. If $1000 is deposited in the plan and the interest is left to accumulate, how much is in the account after 1 year? EXAMPLE 1 Solution Use the simple interest formula, = I Prt. The principal P is $1000 and the rate of interest is = 2% 0.02. After the first quarter of a year, the time t is 1 4 year, so the interest earned is = = ⋅ ⋅ = I Prt $1000 0.02 1 4 $5 (continued) *Some banks use a 360-day “year.” Why do you think they do?
RkJQdWJsaXNoZXIy NjM5ODQ=