Sharp CS-2800 CS-2850/2800 Operation Manual - Page 29

COMPOUND INTEREST Calculate the new balance on a deposit which is compounded quarterly for 4 years at a given annual interest rate. SOLUTION: 1. Calculate the quarterly interest rate. 2. Calculate the new balance (principal plus interest) FORMULA: New balance = P (1 + i)" Where P = amount of deposit (principal) i = interest rate per period n = number of years x 4 EXAMPLE: If P = $6,150 i = 5% annum ÷ 4 periods = 0.0125 n = 4 years x 4 periods = 16 Then 6,150 (1 + 0.0125)76 ;.; $7,502.32 (New Balance) (1) -3 -7 - I -o (2) (3) (4) .05 M4 M 0.05 0.0125 A 0.05 + 4- = 0.0125 * Annual int. rate Quarterly int. rate 0.0125A 1.0125 A 0.0125 + 1. + 1.0125 0 (1 + i) 1.0125 1.02515625 A 1.0125 x 1.0125 = 1.02515625 * (1 + i)2 1.02515625 1.02515625 x 1.02515625 = 1.05094533691 A 1.05094533691 * (1 + i)4 x 1.05094533691 1.05094533691 x 1.10448610117A 1.05094533691 = 1.10448610117 * (1 + 1)8 1.10448610117 1.21988954767 A 1.10448610117 x 1.1044.9610117 = 1.21988954767 * (1 + i)t6 t1 6150 Ei 1.21988954767 7,502.32071817 A 1.21988954767 x 6,150- = 7,502.32071817 * Principal New balance 27