In 7 years Sally needs a total of 110000 so that she can buy

In 7 years, Sally needs a total of $110,000 so that she can buy an exotic sailboat. How much money should she invest into an account today to achieve her goal? The annual interest rate is 2.6% and interest is compounded weekly.

Solution

The formula for compound interest is F = P (1+r)^t where P is the initial anount, F is the maturity value, r is the rate of interest in decimals and t is the number of intervals Here, F = $ 110000, r = (2.6/100)* 1/52 = 1.0005 ( there are 52 weeks in an year) and t = 7*52 = 364. Therefore, 110000 = P( 1+ 0.0005)³⁶⁴  = P( 1.0005)³⁶⁴ = P( 1.199559631). Therefore, P = 110000/ (1.199559631) = 91700.31831 = $ 91700.32 ( approximately, on rounding off to the nearest cent)