Question

1. A demand loan for ​$9565.91 with interest at 9.6​% compounded monthly is repaid after 7 ​years, 2 months. What is the amount of interest​ paid?

2. An investment of ​$3910.75 earns interest at 6.9​% per annum compounded annually for 2 years. At that time the interest rate is changed to 9% compounded monthly. How much will the accumulated value be 1.5 years after the​ change?

Answer 1

Solution:-

1. Given,

Loan = $9,565.91

rate = 9.6%

time = 7years and 2 months

Amount = Loan * (1+r/n)^nt

= $9,565.91 * (1+0.096/12)⁸⁶

= $9,565.91 * (1+0.008)⁸⁶

= $9,565.91 * 1.008⁸⁶

= $9,565.91 * 1.984292

= $18,981.55868

Interest = Amount - Loan

= $18,981.55868 - $9565.91

= $9,415.64868

Therefore the interest is $9,415.65

2. Given,

Initial principal amount = $3,910.75

initial interest rate = 6.9% or 0.069

time = 2 years

Amount = $3,910.75 * (1+0.069)²

= $3,910.75 * 1.069²

= $3,910.75 * 1.142761

= $4,469.05258

After 2 years,new interest rate will be applied,

interest rate = 9% or 0.09

compounded monthly so n= 12

time = 1.5years

Therefore final amount after 1.5 years will be

A = $4,469.05 * (1+0.09/12)^1.5*12

= $4,469.05 * 1.0075¹⁸

= $4,469.05 * 1.14396

= $5,112.41143

Therefore the accumulated value after 1.5 years will be $5,112.41